نتایج جستجو برای: banach a module
تعداد نتایج: 13446897 فیلتر نتایج به سال:
Continuing the research on the Banach-Saks and Schur properties started in (cf. [10]) we investigate analogous properties in the module context. As an environment serves the class of Hilbert C∗-modules. Some properties of weak module topologies on Hilbert C∗-modules are described. Natural module analogues of the classical weak Banach-Saks and the classical Schur properties are defined and studi...
Completely continuous operators Let A be a Banach algebra with |A| % {1}, where A := {a ∈ A : |ab| = |a| |b| for all b ∈ A} is the set of all multiplicative units in A (equivalently, A = {a ∈ A : |a| |a| = 1}). Then for any Banach modules M,N over A, an A-linear map L : M → N is continuous iff supm6=0 |L(m)| |m| < ∞. Let BA(M,N) be the space of such maps. With the norm |L| := supm6=0 |L(m)| |m|...
Let $A$ be a Banach ternary algebra over a scalar field $Bbb R$ or $Bbb C$ and $X$ be a ternary Banach $A$--module. Let $sigma,tau$ and $xi$ be linear mappings on $A$, a linear mapping $D:(A,[~]_A)to (X,[~]_X)$ is called a Lie ternary $(sigma,tau,xi)$--derivation, if $$D([a,b,c])=[[D(a)bc]_X]_{(sigma,tau,xi)}-[[D(c)ba]_X]_{(sigma,tau,xi)}$$ for all $a,b,cin A$, where $[abc]_{(sigma,tau,xi)}=ata...
We first study some properties of $A$-module homomorphisms $theta:Xrightarrow Y$, where $X$ and $Y$ are Fréchet $A$-modules and $A$ is a unital Fréchet algebra. Then we show that if there exists a continued bisection of the identity for $A$, then $theta$ is automatically continuous under certain condition on $X$. In particular, every homomorphism from $A$ into certain Fr...
In a recent paper, S.-E. Takahasi defined the notion of a BSE Banach module over a commutative Banach algebra A with bounded approximate identity. We show that the multiplier space &f(X) of X can be represented as a space of sections in a bundle of Banach spaces, and we use bundle techniques to obtain shorter proofs of various of Takahasi’s results on P-algebra modules and to answer several que...
Let X be a compact Hausdorff space, E be a normed space, A(X,E) be a regular Banach function algebra on X , and A(X,E) be a subspace of C(X,E) . In this paper, first we introduce the notion of localness of an additive map S:A(X,E) → C(X,E) with respect to additive maps T1,...,Tn: A(X) → C(X) and then we characterize the general form of such maps for a certain class of subspaces A(X,E) of C(...
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