相关论文: Hilbert C*-modules and related subjects - a guided…

A $C^*$-textile dynamical system $({\cal A}, \rho,\eta,\Sigma^\rho,\Sigma^\eta, \kappa)$ connsists of a unital $C^*$-algebra ${\cal A}$, two families of endomorphisms ${\rho_\alpha}_{\alpha \in \Sigma^\rho}$ and ${\eta_a}_{a \in…

This paper studies the problems of embedding and isomorphism for countably generated Hilbert C*-modules over commutative C*-algebras. When the fibre dimensions differ sufficiently, relative to the dimension of the spectrum, we show that…

We study two notions of largeness for closed submodules of Hilbert C*-modules: essentiality and topological essentiality. While the analogous properties are known to be equivalent for closed two-sided ideals of C*-algebras, the one-sided…

In this paper, we investigate the structure of the multiplier module of a Hilbert module over a locally C*-algebra and the relationship between the set of all adjointable operators from a Hilbert A-module E to a Hilbert A-module F and the…

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module…

In this paper we introduce the concepts of atomic systems for operators and K-frames in Hilbert C*-modules and we establish some results.

We introduce and study some new uniform structures for Hilbert $C^*$-modules over an algebra $A$. In particular, we prove that in some cases they have the same totally bounded sets. To define one of them, we introduce a new class of…

Let $\{T_1, \ldots, T_n\}$ be a set of $n$ commuting bounded linear operators on a Hilbert space $\mathcal{H}$. Then the $n$-tuple $(T_1, \ldots, T_n)$ turns $\mathcal{H}$ into a module over $\mathbb{C}[z_1, \ldots, z_n]$ in the following…

We give a comprehensive introduction to a general modular frame construction in Hilbert C*-modules and to related modular operators on them. The Hilbert space situation appears as a special case. The reported investigations rely on the idea…

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We give an explicit axiomatization for this theory and describe the structure of all the representations which are…

We introduce the notion of Hilbert $C^*$-module independence: Let $\mathscr{A}$ be a unital $C^*$-algebra and let $\mathscr{E}_i\subseteq \mathscr{E},\,\,i=1, 2$, be ternary subspaces of a Hilbert $\mathscr{A}$-module $\mathscr{E}$. Then…

Let $\cal M$ be a Banach C*-module over a C*-algebra $A$ carrying two $A$-valued inner products $< .,. >_1$, $<.,. >_2$ which induce equivalent to the given one norms on $\cal M$. Then the appropriate unital C*-algebras of adjointable…

We single out the concept of concrete Hilbert module over a locally $C^*$-algebra by means of locally bounded operators on certain strictly inductive limits of Hilbert spaces. Using this concept, we construct an operator model for all…

Our main goal in this paper, is to generalize to Hilbert C*-modules the concept of fusion frames. Indeed we introduce the notion of *\~nfusion frames associated to weighted sequences of orthogonally complemented submodules of a Hilbert…

The aim of the present paper is to describe self-duality and C*- reflexivity of Hilbert {\bf A}-modules $\cal M$ over monotone complete C*-algebras {\bf A} by the completeness of the unit ball of $\cal M$ with respect to two types of…

In this paper, we show that every completely semi-$\phi$-map on a submodule of a Hilbert $C^*$-module has a completely semi-$\phi$-map extension on the whole of module. We also investigate the extendability of $\phi$-maps and provide…

We provide the definition and fundamental properties of algebraic elements with respect to an operator satisfying hypothesis (h). Furthermore, we analyze Hilbert modules using C_0-operators relative to a bounded finitely connected region…

A $\Sigma^*$-algebra is a concrete $C^*$-algebra that is sequentially closed in the weak operator topology. We study an appropriate class of $C^*$-modules over $\Sigma^*$-algebras analogous to the class of $W^*$-modules (selfdual…

This study aims at combining the concepts of $g$-frame and $K$-frame for a Hilbert $C^*$-module $U$, for an operator $K \in End^*_A(U)$, where $End^*_A(U)$ contains all adjointable $A$-linear maps on $U$. As a result, continuous…

A commuting $n$-tuple $(T_1, \ldots, T_n)$ of bounded linear operators on a Hilbert space $\clh$ associate a Hilbert module $\mathcal{H}$ over $\mathbb{C}[z_1, \ldots, z_n]$ in the following sense: \[\mathbb{C}[z_1, \ldots, z_n] \times…