multiplication operators on banach modules over spectrally separable algebras
Authors
abstract
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 $pa$.
similar resources
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...
full textOn the Finsler modules over H-algebras
In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.
full textSpectrally Bounded Operators on Simple C∗-algebras
A linear mapping T from a subspace E of a Banach algebra into another Banach algebra is called spectrally bounded if there is a constant M ≥ 0 such that r(Tx) ≤ M r(x) for all x ∈ E, where r( · ) denotes the spectral radius. We prove that every spectrally bounded unital operator from a unital purely infinite simple C∗-algebra onto a unital semisimple Banach algebra is a Jordan epimorphism.
full textMatrix multiplication operators on Banach function spaces
Let (Ω,Σ,μ) be a σ -finite complete measure space and C be the field of complex numbers. By L(μ ,CN), we denote the linear space of all equivalence classes of CN-valued Σ-measurable functions on Ω that are identified μ-a.e. and are considered as column vectors. Let M◦ denote the linear space of all functions in L(μ ,CN) that are finite a.e. With the topology of convergence in measure on the set...
full texton the finsler modules over h-algebras
in this paper, applying the concept of generalized a-valued norm on a right h - module and also the notion of ϕ-homomorphism of finsler modules over c -algebras we rst improve the de nition of the finsler module over h -algebra and then de ne ϕ-morphism of finsler modules over h -algebras. finally we present some results concerning these new ones.
full textHilbert modules over pro-C*-algebras
In this paper, we generalize some results from Hilbert C*-modules to pro-C*-algebra case. We also give a new proof of the known result that l2(A) is aHilbert module over a pro-C*-algebra A.
full textMy Resources
Save resource for easier access later
Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۵، صفحات ۱۱۵۵-۱۱۶۷
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023