Homepage Gary Weiss

Recent 2014-2020

• Universal Block Tridiagonalization in B(H) and Beyond, Sasmita Patnaik, Srdjan Petrovic and Gary Weiss. The Mathematical Legacy of Victor Lomonosov. Operator theory, De Gruyter, 2020, pp. 317-326. arXiv: 1905.00823. ISBN: 978-3-11-065339-7/hbk; 978-3-11-065675-6/ebook. DOI: 10.1515/9783110656756
• Interplay of Simple and Selfadjoint-Ideal Semigroups in B(H), Sasmita Patnaik and Gary Weiss, Operators and Matrices (OAM), 2020, to appear. arXiv: 1806.01272.
• On diagonals of operators: selfadjoint, normal and other classes, Jireh Loreaux and Gary Weiss, Operator Theory: Themes and Variations. Proceedings of the 27 International Conference on Operator Theory, Timişoara, Romania, 2018, to appear. arXiv: 1905.09987.
• Interplay of Simple and Selfadjoint-Ideal Semigroups in B(H): a survey, Sasmita Patnaik and Gary Weiss, Operator Theory: Themes and Variations. Proceedings of the 27 International Conference on Operator Theory, Timişoara, Romania, 2018, to appear.
• J. Jasper, J. Loreaux and G. Weiss, Thompson's Theorem for compact operators and diagonals of unitary operators, Indiana University Math J., 67 (2018), pp.1–27.
• J. Loreaux and G. Weiss, Traces on ideals and the commutator property, Operator Theory: Themes and Variations. Proceedings of the 26 International Conference on Operator Theory, Timişoara, Romania, 2016, (2018) pp. 145–153. arXiv: 1712.06702 [math.FA]
• J. Loreaux and G. Weiss, An infinite dimensional Schur-Horn Theorem for positive compact operators with nonzero kernel, J. Functional Analysis, Volume 268, Issue 3, 2015, 703–731.
• J. Loreaux and G. Weiss, Diagonality and idempotents with applications to problems in operator theory and frame theory, J. Operator Theory, 75:1(2016), 91–118.
• D. Beltita, S. Patnaik and G. Weiss, On Cartan subalgebras of operator ideals, Indiana University Math J. 65 (2016), 1-37.
• S. R. Garcia, D. Sherman and G. Weiss, On the similarity of $AB$ and $BA$ for normal matrices, Linear Algebra and its Applications, 508 (2016), 14-21.
• S. Patnaik and G. Weiss, A survey on subideals of operators and an introduction to subideal-traces. Birkhauser/Springer: Operator Theory in Harmonic and Non‐commutative Analysis. Operator Theory: Advances and Applications Volume 240, 2014, pp 221-234. 23rd International Workshop in Operator Theory and its Applications.
• D. Beltita, S. Patnaik and G. Weiss, $B(H)$-commutators: A historical survey II and recent advances on commutators of compact operators. In: D. Gaspar, D. Timotin, F.-H. Vasilescu, and L. Zsidó (eds.), The Varied Landscape of Operator Theory (Conference Proceedings, Timisoara, July 2-7, 2012), Theta, Bucharest, 2014, pp. 57-75.
• D. Beltita, S. Patnaik and G. Weiss, Interplay between Algebraic Groups, Lie Algebras and Operator Ideals. In: D. Gaspar, D. Timotin, F.-H. Vasilescu, and L. Zsidó (eds.), The Varied Landscape of Operator Theory (Conference Proceedings, Timisoara, July 2-7, 2012), Theta, Bucharest, 2014, pp. 77-97.

Publications 1996-2013

• S. Patnaik and G. Weiss, Subideals of operators II, J. Integral Equations and Operator Theory, December 2012, Volume 74, Issue 4, 587-600.
• S. Patnaik and G. Weiss, Subideals of operators, J. Operator Theory, 70:2(2013), 101–119.
• G. Weiss, A brief survey on
  • Infinite dimensional Schur-Horn theorems and infinite dimensional majorization theory with applications to operator ideals.
  • $B(H)$-subideals of operators
  Algebraic Methods in Functional Analysis, The Victor Shulman Anniversary Volume, Operator Theory: Advances and Applications, Vol. 233 (2014), Birkhauser, 281-294.
• V. Kaftal and G. Weiss, $B(H)$ lattices, density and arithmetic mean ideals, Houston J. Math., 37 (1)(2011), 233-283.
• V. Kaftal and G. Weiss, Majorization and arithmetic mean ideals, Indiana University Math. J., 60 (2011), 1393-1424.
• D. Schmidt, G. Weiss and V. Zarikian, Paving Small Matrices and the Kadison-Singer Extension Problem II - Computational Results, SCIENCE CHINA Mathematics: Kadison Proceedings, Volume 54, Number 11 (2011), 2463-2472.
  Supplemental numerical data/software and instructions. Science China link to abstract and pdf.
• V. Kaftal and G. Weiss, An infinite dimensional Schur-Horn theorem and majorization theory,J. Functional Analysis, 259 (2010) 3115-3162.
• V. Kaftal and G. Weiss, Traces on operator ideals and arithmetic means, J. Operator Theory, 63 Issue 1, Winter 2010, 3-46.
• G. Weiss and V. Zarikian, Paving Small Matrices and the Kadison-Singer Extension Problem, Operators and Matrices, Vol. 4, no. 3, (2010), 301-352.
• V. Kaftal and G. Weiss, A survey on the interplay between arithmetic mean ideals, traces, lattices of operator ideals, and an infinite Schur-Horn majorization theorem. Hot Topics in Operator Theory, Theta 2008, 101-135.
• V. Kaftal and G. Weiss, Soft ideals and arithmetic mean ideals, Int. Eq. Oper. Theory. 58 (2007) 363-405.
• V. Kaftal and G. Weiss, Second order arithmetic means in operator ideals, Operators and Matrices 1, 2 (2007), 235-256.
• G. Weiss, Commutators – A historical survey, Recent Advances in Operator Theory, Operator Algebras, and their Applications. Oper. Theory Adv. Appl., 153, Birkhäuser, Basel, 2005, 307-320.
• K. Dykema, T. Figiel, G. Weiss and M. Wodzicki, The commutator structure of operator ideals, Adv. Math. 185/1, 2004, 1-79.
• V. Kaftal and G. Weiss, Traces, ideals and arithmetic means, Proc. Natl. Acad. Sci. USA 99, 2002, no. 11, 7356-7360.
• K. Dykema, G. Weiss and M. Wodzicki, Unitarily invariant trace extensions beyond the trace class, Complex analysis and related topics (Cuernavaca, 1996), 59-65, Oper. Theory Adv. Appl., 114, Birkhäuser, Basel, 2000.
• K. Dykema, T. Figiel, G. Weiss and M. Wodzicki, The commutator structure of operator ideals, Institut for Matematik og Datalogi, Odense Universitet, preprint no. 22 (1997), ISSN No. 0903-3920, 1-28.

Kadison-Singer 2006 workshop at American Institute of Mathematics (AIM):

• Report on workshop activities
• Weiss-Zarikian Pre-Workshop Contribution
• Pre-Workshop Contributions
• Material from the workshop
• AIM website

Recent related lecture notes 2006

• G. Weiss and V. Zarikian, 3-Paving Small Matrices and The Kadison-Singer Extension Problem, AIM Workshop Notes.
• G. Weiss and V. Zarikian, 3-paving small matrices and the Kadison-Singer Extension Problem, lecture notes.

Nonselfadjoint Operator Algebras 1992-97

• V. Kaftal, D. Larson and G. Weiss, Quasitriangular subalgebras of semifinite von Neumann algebras are closed, J. Functional Analysis, 107 (1992), no. 2, 387-401.
• M. Bakonyi, V. Kaftal, G. Weiss and H. Woerdeman, Maximum entropy and joint norm bounds for operator extensions. New aspects in interpolation and completion theories, 23-32, Oper. Theory Adv. Appl., 64, Birkhäuser, Basel, 1993.
• M. Bakonyi, V. Kaftal, G. Weiss and H. Woerdeman, Norm bounds for operator extensions, J. Math. Anal. Appl., 194 (1995), no. 2, 352-367.
• M. Bakonyi, V. Kaftal, G. Weiss and H. Woerdeman, Bounds for operator/Hilbert-Schmidt norm minimization using entropy, Indiana Math. J. 46 (1997), no. 2, 405-425.

The Kadison-Singer Extension Problem and The Paving Problem 1985-1990

• H. Halpern, V. Kaftal and G. Weiss, The relative Dixmier property in discrete crossed products, J. Funct. Anal., 69 (1986), no. 1, 121-140. 2-sided version
• H. Halpern, V. Kaftal and G. Weiss, Matrix pavings and Laurent operators, J. Operator Theory 16 (1986), no. 2, 355-374.
• H. Halpern, V. Kaftal and G. Weiss, Matrix pavings in $B(H)$. Operators in indefinite metric spaces, scattering theory and other topics (Bucharest, 1985), 201-214, Oper. Theory Adv. Appl., 24, Birkhäuser, Basel, 1987.
• K. Berman, H. Halpern, V. Kaftal and G. Weiss, Matrix norm inequalities and the relative Dixmier property, Integral Equations Operator Theory 11 (1988), no. 1, 28-48.
• K. Berman, H. Halpern, V. Kaftal and G. Weiss, Some $C_4$ and $C_6$ norm inequalities related to the paving problem. Operator theory: Operator algebras and applications, Part 2 (Durham, NH, 1988), 29-41, Proc. Sympos. Pure Math., 51, Part 2, Amer. Math. Soc., Providence, RI, 1990. 2-sided version

Fuglede-Putnam Theorems 1977-1983

• G. Weiss, The Fuglede commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators I, Trans. Amer. Math. Soc. 246 (1978), 193-209.
• G. Weiss, The Fuglede commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators. Hilbert space operators, Proc. Conf., Calif. State Univ., Long Beach, Calif., (1977), 175-184, Lecture Notes in Math., 693, Springer, Berlin, 1978.
• G. Weiss, An extension of the Fuglede-Putnam theorem modulo the Hilbert-Schmidt class to operators of the form $\sum M_n \times N_n$. Part I. Proceedings of the Fourth Conference on Operator Theory (Timisoara/Herculane, 1979), pp. 105-131, Univ. Timisoara, Timisoara, 1980.
• G. Weiss, The Fuglede commutativity theorem modulo the Hilbert-Schmidt class and generating functions for matrix operators II, J. Operator Theory 5 (1981), no. 1, 3-16.
• G. Weiss, The Fuglede commutativity theorem modulo operator ideals, Proc. Amer. Math. Soc. 83 (1981), no. 1, 113-118.
• R. L. Moore and G. Weiss, The metric Fuglede property and normality, Canad. J. Math. 35 (1983), no. 3, 516-525.
• G. Weiss, An extension of the Fuglede commutativity theorem modulo the Hilbert-Schmidt class to operators of the form $\sum M_n \times N_n$, rans. Amer. Math. Soc. 278 (1983), no. 1, 1-20.

Commutators and ideals 1975-1989

• G. Weiss, Commutators of Hilbert-Schmidt operators and solutions to two problems of Pearcy and Topping. Part II. Proceedings of the Fourth Conference on Operator Theory (Timisoara/Herculane, 1979), 132-140, Univ. Timisoara, Timisoara, 1980.
• G. Weiss, Commutators of Hilbert-Schmidt operators. II, Integral Equations Operator Theory 3 (1980), no. 4, 574-600.
• G. Weiss, Commutators of Hilbert-Schmidt operators. I, Integral Equations Operator Theory 9 (1986), no. 6, 877-892.
• G. Weiss, Classification of certain commutator ideals and the tensor product closure property, Integral Equations Operator Theory 12 (1989), no. 1, 99-128.
• G. Weiss, Commutators and Operator Ideals, dissertation 1975, University of Michigan Microfilm.

Ideals 1976-78

• G. Weiss, Indecomposable Hilbert-Schmidt operators, Proc. Amer. Math. Soc., 56 (1976), 172-176.
• A. Blass and G. Weiss, A characterization and sum decomposition for operator ideals, Trans. Amer. Math. Soc., 246 (1978), 407-417.

With Paul Erdos 1983

• P. Erdos and G. Weiss, Dot product rearrangements. International J. Math. Math. Sci., 6 (1983), no. 3, 409-418.

Miscellaneous 1985-6

• V. Kaftal and G. Weiss, Compact derivations relative to semifinite von Neumann algebras, J. Funct. Anal,. 62 (1985), no. 2, 202-220.
• V. Kaftal and G. Weiss, A Riemann type theorem for unconditional convergence of operators, Proc. Amer. Math. Soc., 98 (1986), no. 3, 431-435.