On the structure of Banach algebras associated with automorphisms. 2. Operators with measurable coefficients
نویسنده
چکیده
In the present paper we continue the study of the structure of a Banach algebra B(A,Tg) generated by a certain Banach algebra A of operators acting in a Banach space D and a group {Tg}g∈G of isometries of D such that TgAT −1 g = A. We investigate the interrelations between the existence of the expectation of B(A,Tg) onto A, metrical freedom of the automorphisms of A induced by Tg and the dual action of the group G on B(A,Tg). The results obtained are applied to the description of the structure of Banach algebras generated by ’weighted composition operators’ acting in Lebesgue spaces. AMS Subject Classification: 47D30, 16W20, 46H15, 46H20
منابع مشابه
On the structure of Banach algebras associated with automorphisms
In the present paper we study the structure of a Banach algebra B(A,Tg) generated by a certain Banach algebra A of operators acting in a Banach space D and a group {Tg}g∈G of isometries of D such that TgAT −1 g = A. We investigate the interrelations between the existence of the expectation of B(A,Tg) onto A, topological freedom of the automorphisms of A induced by Tg and the dual action of the ...
متن کاملLinear operators of Banach spaces with range in Lipschitz algebras
In this paper, a complete description concerning linear operators of Banach spaces with range in Lipschitz algebras $lip_al(X)$ is provided. Necessary and sufficient conditions are established to ensure boundedness and (weak) compactness of these operators. Finally, a lower bound for the essential norm of such operators is obtained.
متن کاملMultiplication 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...
متن کاملPOINT DERIVATIONS ON BANACH ALGEBRAS OF α-LIPSCHITZ VECTOR-VALUED OPERATORS
The Lipschitz function algebras were first defined in the 1960s by some mathematicians, including Schubert. Initially, the Lipschitz real-value and complex-value functions are defined and quantitative properties of these algebras are investigated. Over time these algebras have been studied and generalized by many mathematicians such as Cao, Zhang, Xu, Weaver, and others. Let be a non-emp...
متن کاملSubmajorization inequalities associated with $tau$-measurable operators
The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002