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

被引：7
|
作者：
Briet, Jop [1 ,2 ]
Buhrman, Harry [1 ,2 ]
Lee, Troy [3 ]
Vidick, Thomas [4 ]
机构：
[1] CWI, NL-1098 SJ Amsterdam, Netherlands
[2] Univ Amsterdam, NL-1098 SJ Amsterdam, Netherlands
[3] Ctr Quantum Technol, Singapore 117543, Singapore
[4] Univ Calif Berkeley, Div Comp Sci, Berkeley, CA 94720 USA
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 01期
关键词：
Schatten space; Schur product; Banach algebra; Q-algebra; INEQUALITY; OPERATORS; EXTENSIONS;
D O I：
10.1016/j.jfa.2011.09.001
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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 Perez-Garcia for the trace class, this completes the answer to a long-standing question of Varopoulos. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：1 / 9
页数：9
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