Compact multiplication operators on nest algebras

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...

multiplication operators on banach modules over spectrally separable algebras

‎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...

2 8 A pr 2 00 5 COMPACT OPERATORS AND NEST REPRESENTATIONS OF LIMIT ALGEBRAS ELIAS

In this paper we study the nest representations ρ : A −→ Alg N of a strongly maximal TAF algebra A, whose ranges contain non-zero compact operators. We introduce a particular class of such representations, the essential nest representations , and we show that their kernels coincide with the completely meet irreducible ideals. From this we deduce that there exist enough contractive nest represen...

Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

Composition Operators and Multiplication Operators on Orlicz Spaces

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