All Schatten spaces endowed with the Schur product are Q-algebras

Jop Briët; Harry Buhrman; Troy Lee; Thomas Vidick

doi:10.1016/j.jfa.2011.09.001

All Schatten spaces endowed with the Schur product are Q-algebras

Jop Briët, Harry Buhrman, Troy Lee, Thomas Vidick

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of Pérez-García for the trace class, this completes the answer to a long-standing question of Varopoulos.

Original language	English
Pages (from-to)	1-9
Number of pages	9
Journal	Journal of Functional Analysis
Volume	262
Issue number	1
DOIs	https://doi.org/10.1016/j.jfa.2011.09.001
State	Published - 1 Jan 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1016/j.jfa.2011.09.001

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title = "All Schatten spaces endowed with the Schur product are Q-algebras",

abstract = "We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of P{\'e}rez-Garc{\'i}a for the trace class, this completes the answer to a long-standing question of Varopoulos.",

author = "Jop Bri{\"e}t and Harry Buhrman and Troy Lee and Thomas Vidick",

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AU - Briët, Jop

AU - Buhrman, Harry

AU - Lee, Troy

AU - Vidick, Thomas

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Y1 - 2012/1/1

N2 - We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of Pérez-García for the trace class, this completes the answer to a long-standing question of Varopoulos.

AB - We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of Pérez-García for the trace class, this completes the answer to a long-standing question of Varopoulos.

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U2 - 10.1016/j.jfa.2011.09.001

DO - 10.1016/j.jfa.2011.09.001

M3 - مقالة

SN - 0022-1236

VL - 262

SP - 1

EP - 9

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

All Schatten spaces endowed with the Schur product are Q-algebras

Abstract

All Science Journal Classification (ASJC) codes

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