Determining elements in C*-algebras through spectral properties

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:405

Article

Alaminos, J.¹  Bresar, M.^2,3  Extremera, J.¹  Spenko, S.⁴  Villena, A. R.¹ 

[1] Univ Granada, Fac Ciencias, Dept Anal Matemat, Granada, Spain

[2] Univ Ljubljana, Fac Math & Phys, Ljubljana 61000, Slovenia

[3] Univ Maribor, Fac Nat Sci & Math, Maribor, Slovenia

[4] Inst Math Phys & Mech, Ljubljana, Slovenia

关键词: C*-algebra;    Spectrum;    Spectral radius;   

DOI  :  10.1016/j.jmaa.2013.04.009

来源: Elsevier

【 摘 要 】

Let A be a unital C*-algebra and A '' its second dual. By sigma (a) and r (a) we denote the spectrum and the spectral radius of a is an element of A, respectively. The following two statements hold for arbitrary a, b is an element of A: (1) sigma (ac) subset of sigma(bc) boolean OR {0} for every c is an element of A if and only if there exists a central projection z is an element of A '' such that a = zb, (2) r(ac) <= r(bc) for every c is an element of A if and only if there exists a central element z in A '' such that a = zb and vertical bar vertical bar z vertical bar vertical bar <= 1. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free