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Title
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Almost Multiplicative Maps and epsilon Spectrum of an Element in Frechet Q-Algebra
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Type
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JournalPaper
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Keywords
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Q-algebra, Frechet Q-algebra, almost multiplicative map, epsilon spectrum , almost spectrum
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Abstract
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Let (A; (p_k)) be a Frechet Q-algebra with unit e_A. The epsilon spectrum of an element $x$ in $A$ is defined by sigma_{epsilon}(x) ={r in C: P_{k_0}(re_{A}-x)P_{k_0}(re_{A}-x)^{-1}}>1/epsilon for 0 < epsilon < 1. We show that there is a close relation between the epsilon spectrum and almost multiplicativ maps. It is also shown that {phi(x): phi in M_{alm}}^{c}(A), phi(e_A=1 } is subset of sigma_{epsilon}(x) for every x in A, where M_{alm}}^{c}(A) is the set of all epsilon multiplicative maps from A to C.
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Researchers
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Mohammad Reza Omidi (Second Researcher), Ali Panah Farajzadeh (First Researcher)
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