Conditions equivalent to C* independence

Shuilin Jin; Li Xu; Qinghua Jiang; Li Li

doi:10.4064/sm211-3-1

Conditions equivalent to C* independence

Shuilin Jin
, Li Xu
, Qinghua Jiang^*
, Li Li

^*Corresponding author for this work

Harbin Engineering University

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

2 Scopus citations

Abstract

Let A and B be mutually commuting unital C* subalgebras of B(H). It is shown that A and B are C* independent if and only if for all natural numbers n;m, for all n-tuples A = (A1,.....,An) of doubly commuting nonzero operators of A and m-tuples B = (B1,.....,Bm) of doubly commuting nonzero operators of B, Sp(A;B) = Sp(A)× Sp(B); where Sp denotes the joint Taylor spectrum.

Original language	English
Pages (from-to)	191-197
Number of pages	7
Journal	Studia Mathematica
Volume	211
Issue number	3
DOIs	https://doi.org/10.4064/sm211-3-1
State	Published - 2012

Keywords

C*
Independence
Joint taylor spectrum

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10.4064/sm211-3-1

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title = "Conditions equivalent to C* independence",

abstract = "Let A and B be mutually commuting unital C* subalgebras of B(H). It is shown that A and B are C* independent if and only if for all natural numbers n;m, for all n-tuples A = (A1,.....,An) of doubly commuting nonzero operators of A and m-tuples B = (B1,.....,Bm) of doubly commuting nonzero operators of B, Sp(A;B) = Sp(A)× Sp(B); where Sp denotes the joint Taylor spectrum.",

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T1 - Conditions equivalent to C* independence

AU - Jin, Shuilin

AU - Xu, Li

AU - Jiang, Qinghua

AU - Li, Li

PY - 2012

Y1 - 2012

N2 - Let A and B be mutually commuting unital C* subalgebras of B(H). It is shown that A and B are C* independent if and only if for all natural numbers n;m, for all n-tuples A = (A1,.....,An) of doubly commuting nonzero operators of A and m-tuples B = (B1,.....,Bm) of doubly commuting nonzero operators of B, Sp(A;B) = Sp(A)× Sp(B); where Sp denotes the joint Taylor spectrum.

AB - Let A and B be mutually commuting unital C* subalgebras of B(H). It is shown that A and B are C* independent if and only if for all natural numbers n;m, for all n-tuples A = (A1,.....,An) of doubly commuting nonzero operators of A and m-tuples B = (B1,.....,Bm) of doubly commuting nonzero operators of B, Sp(A;B) = Sp(A)× Sp(B); where Sp denotes the joint Taylor spectrum.

KW - C

KW - Independence

KW - Joint taylor spectrum

UR - https://www.scopus.com/pages/publications/84870589337

U2 - 10.4064/sm211-3-1

DO - 10.4064/sm211-3-1

M3 - 文章

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SN - 0039-3223

VL - 211

SP - 191

EP - 197

JO - Studia Mathematica

JF - Studia Mathematica

IS - 3

ER -

Conditions equivalent to C* independence

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Keywords

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