multiplication operators on banach modules over spectrally separable algebras
نویسندگان
چکیده
let $pa$ be a commutative banach algebra and $ex$ be a left banach $pa$-module. we study the set $dec_{pa}(ex)$ of all elements in $pa$ which induce a decomposable multiplication operator on $ex$. in the case $ex=pa$, $dec_{pa}(pa)$ is the well-known apostol algebra of $pa$. we show that $dec_{pa}(ex)$ is intimately related with the largest spectrally separable subalgebra of $pa$ and in this context we give some results which are related to an open question if apostol algebra is regular for any commutative algebra $pa$.
منابع مشابه
Multiplication operators on Banach modules over spectrally separable algebras
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 s...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۵، صفحات ۱۱۵۵-۱۱۶۷
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