A spectral mapping theorem for Banach modules

• Autorzy: H. Seferoğlu
• Języki publikacji: EN

Abstrakty

EN

Let G be a locally compact abelian group, M(G) the convolution measure algebra, and X a Banach M(G)-module under the module multiplication μ ∘ x, μ ∈ M(G), x ∈ X. We show that if X is an essential L¹(G)-module, then $σ(T_{μ}) = \overline {μ̂(sp(X))}$ for each measure μ in reg(M(G)), where $T_{μ}$ denotes the operator in B(X) defined by $T_{μ}x = μ ∘ x$, σ(·) the usual spectrum in B(X), sp(X) the hull in L¹(G) of the ideal $I_{X} = {f ∈ L¹(G) | T_{f} = 0}$, μ̂ the Fourier-Stieltjes transform of μ, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all the absolutely continuous measures and discrete measures.

Kategorie tematyczne

• 46H15: Representations of topological algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 156
• Numer: 2
• Strony: 99-103

Daty

wydano

2003

Twórcy

autor

H. Seferoğlu

• Department of Mathematics, Faculty of Art and Science, Yüzüncü Yil University, 65080 Van, Turkey

Identyfikatory

DOI

10.4064/sm156-2-1