Multiplication operators on Banach modules over spectrally separable algebras

نویسنده

  • J. ‎Bračič Department of Materials and Metallurgy‎, ‎Faculty of Natural Sciences and Engineering‎, ‎University of Ljubljana‎, ‎Aškerčeva c‎. ‎12‎, ‎SI-1000 Ljubljana‎, ‎Slovenia.
چکیده مقاله:

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We show that ${rm Dec}_{mathcal{A}}(mathscr{X})$ is intimately related with the largest spectrally separable subalgebra of $mathcal{A}$ and in this context‎ ‎we give some results which are related to an open question if Apostol algebra is regular for any commutative algebra $mathcal{A}$‎.‎

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multiplication operators on banach modules over spectrally separable algebras

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عنوان ژورنال

دوره 42  شماره 5

صفحات  1155- 1167

تاریخ انتشار 2016-11-01

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