Faculty & Staff By Last Name

Faculty & Staff By Last Name

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Victor Kaftal

Title: Professor
Office: 5512 French Hall
Tel: 513-556-4091
Email: victor.kaftal@uc.edu

Education

  • Ph.D, Tel Aviv University, Israel, 1979 (Mathematics).
  • Laurea, Universita' degli Studi di Milano, Italy, 1970 (Physics).

Research Information

Research Interests

My main research areas are Operator Theory and Operator Algebras. In recent years,  I have been working mainly on:
• frame theory in B(H) and in C*-modules,
• decomposition of positive operators into positive combinations of projections or into sums of projections, in the setting of B(H), of von Neumann algebras, and of  C*-algebras.
• sums of commutators and linear combination of projections in finite C*-algebras
• strict comparison of projections and of positive elements in C*-algebras

Research Support

  • (PI), Kaftal, Victor, The Eleventh East Coast Operator Algebras Symposium, National Science Foundation. (DMS-1343888), $31,760.00. 08/15/2013 to 07/31/2014. Status: Active.
  • (PI), Victor Kaftal, Collaboration Grants for Mathematicians, Simons Foundation. (245660), 35,000. 09/01/2012 to 08/31/2017. Status: Active.
  • (PI), Halpern, Herbert; Kaftal, Victor; Peligrad, Costel; Weiss, Gary; Zhang, Shuang, Collaborative Research: Operator Theory/Operator Algebras, GPOTS 07-08, National Science Foundation. (DMS-0649960), $25,000.00. 04/01/2007 to 03/31/2009. Status: Closed.
  • (PI), Kaftal, Victor, Finite Sums of Projections, Simons Foundation. (Award Number: 245660), $7,000.00. 09/01/2012 to 08/31/2017. Status: Active.

Publications

Peer Reviewed Publications

  • Kaftal, V P. W. Ng, S. Zhang, Commutators and linear spans of projections in certain finite C*-algebras, Journal Functional Analysis (2014), 266, No 4, 1883-1912.
  • Halpern, H., Kaftal, V., Ng. P.W., Zhang, S. Finite sums of projections in von Neumann algebras, Trans. Amer Math Soc (2013) 365, 2409-2445
  • Kaftal. V., Ng. P.W., Zhang, S. Finite sums of projections in purely infinite simple C*-algebras with torsion K_0, Proc. Amer Math Soc, (2012), 140, No 9, 3219-3227.
  • Kaftal, V., Ng, P.W., Zhang, S.  Projection decompositions in multiplier algebras. Mathematische Annalen,  (2012) 352, No 3, 543-566.
  • Kaftal. V., Ng. P.W., Zhang, S. Positive combinations and sums of projections in purely infinite simple C*-algebras and their multiplier algebras, Proc. Amer Math Soc (2011) 139, 2735-2746.
  • Kaftal, V. & Weiss G.  B(H) Lattices, density, and arithmetic means ideals. Houston J. Math. (2011) 37, 233-283.
  • Kaftal, V. & Weiss G.  Majorization and arithmetic mean ideals. Indiana Univ. Math J., (2011) 60, 1393-1424.
  • Kaftal, V. &Weiss, G.  An infinite dimensional Schur-Horn theorem and majorization theory. J. Funct. Anal. (2010) 259, 3115-3162.
  • Kaftal, V., & Weiss, G.  Traces on operator ideals and arithmetic means. Journal of Operator Theory, (2010) 63, No 1, 3-46
  • Kaftal. V., Ng. P.W., Zhang, S. Strong sums of projections in von Neumann factors. J. Funct. Anal. (2009) 257, 3115-3162
  • Kaftal, V., Larson, D., & Zhang, S. Operator valued frames. Transactions AMS  (2009) 361 (12) 6349-6385.
  • Kaftal, V. & Pal, D.  Does third degree price discrimination reduce social welfare? Southern Economic J. (2008) 75 (2) 558-573.
  • Kaftal, V., Larson, D. & Zhang, S. Operator valued frames on C*-modules. Contemporary Math., (2008) 451, 363-408
  • Kaftal, V., & Weiss, G. Second order arithmetic means in operator ideals. Operators and Matrices (2007) 1,  235-256.
  • Kaftal, V., & Weiss, G.  Soft ideals and arithmetic means. Integral Eq Operator Theory J., (2007) 58, 363-405.
  • Bryc, W., & Kaftal, V. Strong mixing coefficients for non-commutative Gaussian processes. Proc. Amer. Math. Soc, (2003) 132 (2), 523-534.
  • Kaftal, V., & Weiss, G. Traces ideals, and arithmetic means. Proceedings National Academy of Sciences, (2002) 99 (11), 7356-7360.
  • Bakonyi, M., Kaftal, V., Weiss, G., & Woerdeman, H. Bounds for operator/Hilbert Schmidt norm minimization using entropy. Indiana University Math. J,  (1997) 46 (2)  405-426.
  • Bakonyi, M., Kaftal, V., Weiss, G., & Woerdeman, H. Norm bounds for operator extensions. Journal of Mathematical Analysis and Applications, (1995) 194, 352-367.
  • Bakonyi, M, Kaftal, V., Weiss, G., & Woerdeman, H.  Maximum entropy and joint norm bounds for operator extensions. Operator Theory: Advances and Appl, (1993) 64, 23–32.
  • Kaftal, V., Larson, D., & Weiss, G.  Quasitriangular subalgebras of semifinite von Neumann algebras are closed. J. Funct. Anal, (1992) 107 (2), 387-401.
  • Kaftal, V.  Type decompositions for von Neumann algebras embeddings. J. Func. Anal, (1991) 98(1), 169-193.
  • Halpern, H., Kaftal, V., & Zsidó, L. Finite weight projections in von Neumann algebras. Pacific J. Math, (1991) 147(1), 81-121.
  • Berman, K., Halpern, H., Kaftal, V., & Weiss, G.  Matrix norm inequalities and the relative Dixmier property. Int. Eq. and Oper. Th. J., (1988) 11, 28-48.
  • Halpern, H., Kaftal, V., & Weiss, G.  Matrix pavings in B(H). Oper. Th.: Advances and Applications, (1987) 24, 201-214.
  • Halpern, H., & Kaftal, V. Compact operators in type IIIlambda and type IIIo factors, II. Tohôku Math. J., (1987) 39, 153-173.
  • Halpern, H., & Kaftal, V.  Compact operators in type IIIlambda and type IIIo factors. Math. Ann., (1986) 273, 251-270.
  • Kaftal, V., & Mercer, R. Spectral projections of L1-operators in type IIIlambda von Neumann algebras. Integr. Eq. and Oper. Th., (1986) 9, 679-693.
  • Kaftal, V., & Weiss, G. A Riemann type theorem for unconditional convergence of operators. Proc. AMS., (1986) 98, 431-436.
  • Halpern, H., Kaftal, V., & Weiss, G. Matrix pavings and Laurent operators. J. Oper. Th., (1986) 16, 355-374.
  • Halpern, H., Kaftal, V., & Weiss, G. The relative Dixmier property in discrete crossed products. J. Funct. Anal., (1986) 69, 121-140.
  • Kaftal, V., & Weiss, G. Compact derivations relative to semifinite von Neumann algebras. J. Funct. Anal., (1986) 62, 202-220.
  • Cho, S.J., & Kaftal, V. A generalization of the Weyl-von Neumann theorem to semifinite von Neumann algebras. Indiana Univ. Math. J., (1982) 31, 57-63.
  • Kaftal, V. Almost Fredholm operators in von Neumann algebras. Integr. Eq. and Oper. Th., (1982) 5, 50-70.
  • Kaftal, V. Relative weak convergence of vectors in semifinite von Neumann algebras. Proc. AMS., (1982) 84, 89-94.
  • Kaftal, V. On the theory of compact operators in von Neumann algebras II. Pacific J. Math., (1978) 79, 129-137.
  • Kaftal, V. On the theory of compact operators in von Neumann algebras I. Indiana Univ. Math. J., (1977) 26, 447-457.
  • Kaftal, V P. W. Ng, S. Zhang, Strict comparison of projections and positive combinations of projections in certain multiplier algebras. J. Oper. Theory. (2015), 73, No1, 187-210
  • Dragan, C., Kaftal, V., Sums of equivalent sequences of positive operators in von Neumann factors. Houston Journal of Mathematics, (2016), 42, No. 3, 991-1017.
  • Kaftal V, Ng, P.W., Zhang, S., Strict comparison of positive elements in multiplier algebras, to appear Canadian Journal of Mathematics
  • Bemrose, T., Casazza, P. G.,  Kaftal, V. , and Lynch P.G., The unconditional constant for Hilbert space frame expansions, to appear in Linear Algebra and its Applications. (2016)

Peer Reviewed Conference/Workshop Proceedings

  • Kaftal. V., Ng. P.W., Zhang, S. Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras, Science China Mathematics, (2011) 54, 1-10 .
  • Kaftal, V. & Weiss, G. A survey on the interplay between arithmetic ideals, traces, lattices of operator ideals, and an infinite Schur-Horn majorization theorem. Hot topics in Operator Theory, Theta P. (2008) 101-135.
  • Berman, K., Halpern, H., Kaftal, V., & Weiss, G. Some C4 and C6 norm inequalities related to the paving problem. Proceedings of Symposia in Pure Mathematics, (1990) 51(2), 29-41.
  • Halpern, H., Kaftal, V., & Zsidó, L.  Finite weight projections in von Neumann factors. Proceedings of Symposia in Pure Mathematics, (1990) 51(2), 143-152.
  • Kaftal V, Ng, P.W., Zhang, S., Projections in C*-algebras and strict comparison, Hot topics in operator theory, Theta 2016

Presentations & Lectures

Invited Presentations

  • Kaftal V (07-2014). Linear combinations of projections in C*-algebras and their multiplier algebras 25th International Conference on Operator Theory, Timisoara, Romania.
  • Kaftal V (05-2014). Linear combinations of projections in C*-algebras Great Plains Operator Theory Symposium, Kansas State University.
  • Kaftal, V (04-2014). Positive linear combinations of projections AMS Special Sessionon Progress in Noncommutative Analysis, Albuquerque, NM.
  • (02-2013). Positive linear combinations of projections in certain finite C*-algebras and in their multiplier algebras Wabash Seminar, Crawfordsville, IN.
  • (10-2012). Linear combinations of projections in finite C*-algebras 10th ECOAS, Knoxville, TN.
  • (07-2012). Linear combinations of projections 24rth International Conference on Operator Theory,, Timisoara, Romania.
  • (05-2012). Positive combinations of projections Great Plains Operator Theory Symposium (GPOTS), Houston, TX.
  • (05-2011). Finite sums of projections in operator algebras Canadian Operator Symposium 2011, U. Victoria, Victoria, BC.
  • (01-2011). Finite Sums of Projections Special Session AMS Annual Meeting, New Orleans.
  • (01-2011). Equal-norm perturbations of finite frames Workshop in Analysis and Geometry, LSU, Baton Rouge, LA.
  • (07-2010). 23rd Conference in Operator Theory, Timisoara, Romania.
  • (01-2010). AMS Special Session, San Francisco, CA.
  • (01-2010). Workshop on Optimal Frames , San Francisco, CA.
  • (07-2009). GPOTS, Boulder, Co.
  • (03-2009). AMS Special Session, Urbana, IL.
  • (07-2008). 22nd Conference in Operator Theory, Timisoara, Romania.
  • (04-2008). AMS Special Session, Bloomington, IN.
  • (04-2008). Nebraska-Iowa Functional Analysis Seminar, Iowa City, IA.
  • (05-2007). GPOTS, Lincoln, NE.
  • (08-2006). Concentration Week in Analysis, College Station, TX.
  • (01-2006). AMS Special Session, S. Antonio, TX.
  • (07-2003). ICAA, S. Africa.
  • (01-2003). AMS Special Session, Baltimore, MD.
  • (07-2002). Nonselfadjoint Operator Algebras Workshop, Toronto, ON Canada.
  • (07-2001). 18th Conference in Operator Theory, Timisoara, Romania.
  • (06-2001). GPOTS, NH.
  • (04-1999). Nebraska-Iowa Functional Analysis Seminar, Iowa City, IA.
  • (07-1996). IWOTA, Bloomington, IN.
  • (10-1993). AMS Special Session, College Station, TX.
  • (04-1993). Operator Theory and Wavelet Conference, Raleigh, NC.
  • (01-1993). AMS Special Session, S. Antonio, TX.
  • (11-1992). Operator Theory Conference, College Station, TX.
  • (10-1992). AMS Special Session, Dayton, OH.
  • (09-1991). Wabash Seminar, Crawforsdville, IN.
  • (05-1991). GPOTS, College Station, TX.
  • (04-1991). Wabash Conference, Indianapolis, IN.
  • (01-1991). AMS Special Session, San Francisco, CA.
  • (05-1990). GPOTS, Albuquerque, NM.
  • (07-1988). 36th AMS Summer Research Institute Durham, NH.
  • (05-1988). GPOTS, Indianapolis, IN.
  • (10-1987). AMS Special Session, Lincoln, NE.
  • (08-1986). International Congress of Mathematicians, Berkeley, CA.
  • (07-1985). 10th International Conference in Operator Theory, Bucharest, Romania.
  • (05-1985). GPOTS, College Station, TX.
  • (05-1984). GPOTS, Ames, IA.
  • Kaftal V. (05-2015). Ideals in multiplier algebras of simple finite C*-algebras Great Plain Operator Theory Symposium, West Lafayette.
  • (06-1983). GPOTS, Boulder, CO.
  • Kaftal, V (07-2016). The integer in Kadison's Pythagorean Theorem and essential codimension. 25th Conference in Operator Theory, Timisoara, Romania.
  • (08-1980). Summer Research Institute on Operator Algebras, Kingston, ON Canada.
  • Kaftal, V (05-2016). The integer in Kadison's Pythagorean Theorem and essential codimension. Great Plains Operator theory Seminar, Urbana, IL.
  • (12-1979). Wabash Seminar, Crawforsdville, IN.
  • (05-1979). Israel Math Soc, Beer Sheva, Israel.
  • (01-1979). AMS , Biloxi, MS.

Lectures

  • (01-2008). U. Rome Tor Vergata, Rome, Italy.
  • (11-2014). Linear combinations of projections in operator algebras. University Virginia, Charlottestville.
  • (11-2007). U. Louisiana, Lafayette, LA.
  • (11-2014). Compact operators in type III factors. University Virginia, Charlottestville, VA.
  • (11-2007). Texas A&M Analysis Seminar, College Station, TX.
  • (10-2014). Frame theory methods in Kadison's Pythagorean theorem and in sums of projections problems. University Houston, Houston, TX.
  • (12-2001). U. Rome Tor Vergata, Rome, Italy.
  • (10-2014). The role of the frame transform and its Fredholm index in various operator theory problems.. Texas A&M , College Station, TX.
  • (04-1999). U. Waterloo, Waterloo, ON Canada.
  • (09-2014). Intriguing integers in some operator theory problems. University Louisiana, Lafayette, LA.
  • (04-1999). U. Nebraska, Lincoln, NE.
  • (02-1999). Texas A&M University, College Station, TX.
  • (1990). Wright State University, Dayton, OH.
  • (02-1989). University of Houston, Houston, TX.
  • (03-2013). Linear combinations of projections in C* and W* algebras. Texas A&M, College Station, TX.
  • (01-1989). Texas A&M University, College Station, TX.
  • (11-1988). University of Pennsylvania, Philadelphia, PA.
  • (12-1986). Polythechnic of Milan, Milan, Italy.
  • (1986). University of Milan, Milan, Italy.
  • (09-1985). Stuttgart University, Stuttgart, West Germany.
  • (09-1985). Copenhagen University, Copenhagen, Denmark.
  • (11-1984). Mathematical Sciences Research Institute, Berkeley, CA.
  • (11-1984). UCLA, Los Angeles. CA.
  • (12-1983). Kepler University, Linz, Austria.
  • (12-1983). Joint Mathematical-Physical Seminar of Milan, Milan, Italy.
  • (1983). University of Milan, Milan, Italy.
  • (12-1981). Polythechnic of Milan, Italy.
  • (12-1981). Joint Mathematical-Physical Seminar of Milan, Milan, Italy.
  • (02-1981). Texas A&M University, College Station, TX.
  • (05-1980). University of Georgia, Athens, GA.
  • (03-1980). SUNY at Stony Brook, New York, NY.
  • (02-1979). Dalhousie University, Halifax, NS Canada.
  • (02-1979). Purdue University, West Lafayette, IN.
  • (02-1979). Toronto University, Toronto, ON Canada.
  • (1979). York University, Toronto, ON Canada.
  • (01-2015). The role of finiteness of the tracial simplex for certain C*-algebras and their multiplier algebras. University Waterloo.

Experience & Service

Work Experience

  • 1979 to 1981, Visiting Assistant Professor, University of Cincinnati.
  • 1981 to 1985, Assistant Professor, University of Cincinnati.
  • 09-1984 to 12-1984, Member, Mathematical Sciences Research Institute, Berkeley, CA.
  • 1985 to 1991, Associate Professor, University of Cincinnati.
  • 09-1988 to 03-1989, Visiting Scholar, University of Pennsylvania, Philadelphia, PA & , Texas A&M University, College Station, TX.
  • 1991 to Present, Professor,.
  • 09-1998 to 03-1999, Visiting Scholar, Texas A&M Univ, College Station, TX; U. Waterloo, Ontario;, U. Nebraska, Lincoln, NE.
  • 09-2007 to 03-2008, Visiting Scholar, Texas A&M Univ, College Station, TX;, Univ. Roma, Tor Vergata, Roma, Italy.
  • 09-2014 to 10-2014, Visiting Scholar, University Lousiana, Lafayette, LA.
  • 10-2014 to 11-2014, Visting Scholar, Texas A&M University, College Station, TX.

Service

  • Coordinator of the Calculus Sequence for 2011-2013, 09-2011
  • Member, A&S Senate, 09-2011
  • Committee Chair, Coordinator of Calculus, 09-2011
  • Committee Chair, Coordinator of Calculus, 09-2011
  • Member, A&S Senate, 09-2011
  • Committee Chair, Academic Program Review Committee, 09-2011 to 06-2012
  • Committee Chair, Calculus Committee, 07-2011
  • Committee Chair, Graduate Advisors Committee , 09-2010 to 08-2011
  • Committee Chair, Graduate Affairs Committee, 09-2010 to 08-2011

Courses Taught

  • Real Analysis
    Real Analysis
    Level: Graduate
    Term: 11W
    Comments: In parallel to the course, weekly preparatory sessions for the preliminary examination based on the course
  • 15-MATH-252 CALCULUS II
    Level: Undergraduate
    Term: 11U

  • 15-STAT-241 INTRO TO STATISTICS
    Level: Undergraduate
    Term: 11U

  • Real Analysis
    Real Analysis
    Level: Graduate
    Term: 11S
    Comments: In parallel to the course, weekly preparatory sessions for the preliminary examination based on the course
  • 15-MATH-251 CALCULUS I
    Level: Undergraduate
    Term: 11A

  • 15-MATH-251 CALCULUS I
    Level: Undergraduate
    Term: 11A

  • 15-MATH-252 CALCULUS II
    Level: Undergraduate
    Term: 12W

  • 15-MATH-253 CALCULUS III
    Level: Undergraduate
    Term: 11S

  • Calculus 1
    Calculus 1
    Level: Undergraduate
    Term: 12FS