Determining elements in Banach algebras through spectral properties

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Bresar, Matej^1,2  Spenko, Spela³ 

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

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

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

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

DOI  :  10.1016/j.jmaa.2012.03.058

来源: Elsevier

【 摘 要 】

Let A be a Banach algebra. By sigma(x) and r(x), we denote the spectrum and the spectral radius of x is an element of A, respectively. We consider the relationship between elements a, b is an element of A that satisfy one of the following two conditions: (1) sigma(ax) = sigma(bx) for all x is an element of A, (2) r(ax) <= r(bx) for all x is an element of A. In particular, we show that (1) implies that a = b if A is a C*-algebra, and (2) implies that a is an element of Cb if A is a prime C*-algebra. As an application of the results concerning the conditions (1) and (2), we obtain some spectral characterizations of multiplicative maps. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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