Browsing by Author "Seferoglu, H"

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    Article
    A Spectral Mapping Theorem for Banach Modules
    (Polish Acad Sciences inst Mathematics, 2003) Seferoglu, H
    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 muox, mu is an element of M(G), x is an element of X. We show that if X is an essential L-1 (G)-module, then sigma(T-mu) = (μ) over cap (sp(X)) for each measure mu in reg(M(G)), where T-mu denotes the operator in B(X) defined by T(mu)x = mu o x, sigma(.) the usual spectrum in B(X), sp(X) the hull in L-1(G) of the ideal I-X = {f is an element of L-1(G) \ T-f = 0}, the Fourier-Stieltjes transform of mu, and reg(M(G)) the largest closed regular subalgebra of M(G); reg(M(G)) contains all the absolutely continuous measures and discrete measures.
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    Article
    A Spectral Mapping Theorem for Representations of One-Parameter Groups
    (Amer Mathematical Soc, 2006) Seferoglu, H
    In this paper we present some generalization (at the same time a new and a short proof in the Banach algebra context) of the Weak Spectral Mapping Theorem (WSMT) for non-quasianalytic representations of one-parameter groups.