Multiplication operators on Banach modules over spectrally separable algebras
نویسنده
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 $mathcal{A}$.
منابع مشابه
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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