Unital strongly harmonic commutative Banach algebras

• Autorzy: Janko Bračič
• Języki publikacji: EN

Abstrakty

EN

A unital commutative Banach algebra 𝓐 is spectrally separable if for any two distinct non-zero multiplicative linear functionals φ and ψ on it there exist a and b in 𝓐 such that ab = 0 and φ(a)ψ(b) ≠ 0. Spectrally separable algebras are a special subclass of strongly harmonic algebras. We prove that a unital commutative Banach algebra 𝓐 is spectrally separable if there are enough elements in 𝓐 such that the corresponding multiplication operators on 𝓐 have the decomposition property (δ). On the other hand, if 𝓐 is spectrally separable, then for each a ∈ 𝓐 and each Banach left 𝓐 -module 𝒳 the corresponding multiplication operator $L_{a}$ on 𝒳 is super-decomposable. These two statements improve an earlier result of Baskakov.

Kategorie tematyczne

• 47B48: Operators on Banach algebras
• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
• 46J05: General theory of commutative topological algebras

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 3
• Strony: 253-266

Daty

wydano

2002

Twórcy

autor

Janko Bračič

• IMFM, University of Ljubljana, Jadranska 19, 1111 Ljubljana, Slovenia

Identyfikatory

DOI

10.4064/sm149-3-3