Scattered elements of Banach algebras

• Autorzy: Peng Cao
• Języki publikacji: EN

Abstrakty

EN

A scattered element of a Banach algebra 𝓐 is an element with at most countable spectrum. The set of all scattered elements is denoted by 𝓢(𝓐). The scattered radical $𝓡_{sc}(𝓐)$ is the largest ideal consisting of scattered elements. We characterize in several ways central elements of 𝓐 modulo the scattered radical. As a consequence, it is shown that the following conditions are equivalent: (i) 𝓢(𝓐) + 𝓢(𝓐) ⊂ 𝓢(𝓐); (ii) 𝓢(𝓐)𝓢(𝓐) ⊂ 𝓢(𝓐); (iii) $[𝓢(𝓐),𝓐] ⊂ 𝓡_{sc}(𝓐)$.

Kategorie tematyczne

• 47B06: Riesz operators; eigenvalue distributions; approximation numbers, s -numbers, Kolmogorov numbers, entropy numbers, etc. of operators
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 214
• Numer: 2
• Strony: 195-200

Daty

wydano

2013

Twórcy

autor

Peng Cao

• School of Mathematics, Beijing Institute of Technology, Beijing, China
• Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing, China, 100081

Identyfikatory

DOI

10.4064/sm214-2-6