Abstract
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 Rsc(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] ⊂ Rsc(A).
Original language | English |
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Pages (from-to) | 195-200 |
Number of pages | 6 |
Journal | Studia Mathematica |
Volume | 214 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2013 |
Keywords
- Jacobson radical
- Scattered element
- Scattered radical
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Cao, P. (2013). Scattered elements of Banach algebras. Studia Mathematica, 214(2), 195-200. https://doi.org/10.4064/sm214-2-6