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pro vyhledávání: '"Sinclair, Thomas"'
Autor:
Sinclair, Thomas, Vivek, Naveen
The goal of this short note is to point out three observations around the Grothendieck norm and semidefinite programming. The first is that the Grothendieck norm captures the difficulty of relating the off-diagonal entries of a real, symmetric matrix
Externí odkaz:
http://arxiv.org/abs/2210.03868
Autor:
Sinclair, Thomas
We survey the model theory of operator systems and C$^*$-algebras.
Comment: Comments welcome! A finalized version will appear in the volume "Model Theory of Operator Algebras." The manuscript references other contributions to that volume
Comment: Comments welcome! A finalized version will appear in the volume "Model Theory of Operator Algebras." The manuscript references other contributions to that volume
Externí odkaz:
http://arxiv.org/abs/2210.03862
Inspired by a well-known characterization of the index of an inclusion of II$_1$ factors due to Pimsner and Popa, we define an index-type invariant for inclusions of operator systems. We compute examples of this invariant, show that it is multiplicat
Externí odkaz:
http://arxiv.org/abs/2203.05710
Publikováno v:
Linear Algebra Appl. 663 (2023), 178-199
Using techniques from semidefinite programming, we study the problem of finding a closest quantum channel to the projection onto a matricial subsystem. We derive two invariants of matricial subsystems which are related to the quantum Lov\'asz theta f
Externí odkaz:
http://arxiv.org/abs/2203.02627
We show that there is an operator space notion of Lipschitz embeddability between operator spaces which is strictly weaker than its linear counterpart but which is still strong enough to impose linear restrictions on operator space structures. This s
Externí odkaz:
http://arxiv.org/abs/2104.02714
Publikováno v:
In Water Research 1 January 2024 248
Autor:
Mulcahy, Garrett, Sinclair, Thomas
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022), no. 7, 2969-2982
We exhibit an operator norm bounded, infinite sequence $\{A_n\}$ of $3n \times 3n$ complex matrices for which the commutator map $X\mapsto XA_n - A_nX$ is uniformly bounded below as an operator over the space of trace-zero self-adjoint matrices equip
Externí odkaz:
http://arxiv.org/abs/2009.11139
This paper gives a free entropy theoretic perspective on amenable absorption results for free products of tracial von Neumann algebras. In particular, we give the first free entropy proof of Popa's famous result that the generator MASA in a free grou
Externí odkaz:
http://arxiv.org/abs/1912.11569