Related papers: A Riesz-Fredholm type theorem on certain Hilbert C…

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…

For a $C^*$-algebra $A$ of compact operators and a compact manifold $M,$ we prove that the Hodge theory holds for $A$-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective $A$-Hilbert…

Let $E \subset \mathbb{C}$ be a Borel set such that $0<\mathcal{H}^1(E)<\infty$. David and L\'eger proved that the Cauchy kernel $1/z$ (and even its coordinate parts $\textrm{Re}\, z/|z|^2$ and $\textrm{Im}\, z/|z|^2$, $z\in…

A regular operator T on a Hilbert C^*-module is defined just like a closed operator on a Hilbert space, with the extra condition that the range of (I+T^*T) is dense. Semiregular operators are a slightly larger class of operators that may…

In this paper, a spectral theorem is proved for self-adjoint cyclically compact partial integral operators in the space of functions with mixed norm, which is a Kaplansky--Hilbert module. The decomposition through eigenfunctions, integral…

Let $\varphi$ be a linear-fractional, non-automorphism self-map of $\mathbb{D}$ that fixes $\zeta \in \mathbb{T}$ and satisfies $\varphi^{\prime}(\zeta) \neq 1$ and consider the composition operator $C_{\varphi}$ acting on the Hardy space…

Suppose $A$ is a pro-C*-algebra. Let $L_{A}(E)$ be the pro-C*-algebra of adjointable operators on a Hilbert $A$-module $E$ and let $K_{A}(E)$ be the closed two sided $*$-ideal of all compact operators on $E$. We prove that if $E$ be a full…

Let $(R, \mf, k_R)$ be regular local $k$-algebra satisfying the weak Jacobian criterion, such that $k_R/k$ is an algebraic field extension. Let $D_R$ be the ring of $k$-linear differential operators of $R$. We give an explicit decomposition…

We extend the symbol calculus and study the limit operator theory for $\sigma$-compact, \'{e}tale and amenable groupoids, in the Hilbert space case. This approach not only unifies various existing results which include the cases of exact…

As a partial generalisation of the Uhlhorn theorem to Hilbert $C^*$-modules, we show in this article that the module structure and the orthogonality structure of a Hilbert $C^*$-module determine its Hilbert $C^*$-module structure. In fact,…

We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for…

In this paper we consider A-Fredholm and semi-A-Fredholm operators on Hilbert C*-modules over a W*-algebra A defined in [3],[10]. Using the assumption that A is a W*-algebra (and not an arbitrary C*-algebra), we obtain several results such…

We extend a work of Pedersen and Takesaki by giving some equivalent conditions for the existence of a positive solution of the so-called Pedersen--Takesaki operator equation $XHX=K$ in the setting of Hilbert $C^*$-modules. It is known that…

In this paper we study the unitary equivalence between Hilbert modules over a locally C*-algebra. Also, we prove a stabilization theorem for countably generated modules over an arbitrary locally C*-algebra and show that a Hilbert module…

The main goal of the present paper is to generalize the results of~\cite{TroLNM,TroBoch} in the following way: To be able to define $K_0(A)\o\C$-valued Lefschetz numbers of the first type of an endomorphism $V$ on a C*-elliptic complex one…

Let $\mathcal{L}(\mathscr{H})$ denote the $C^*$-algebra of adjointable operators on a Hilbert $C^*$-module $\mathscr{H}$. We introduce the generalized Cauchy-Schwarz inequality for operators in $\mathcal{L}(\mathscr{H})$ and investigate…

Let $E \subset \C$ be a Borel set with finite length, that is, $0<\mathcal{H}^1 (E)<\infty$. By a theorem of David and L\'eger, the $L^2 (\mathcal{H}^1 \lfloor E)$-boundedness of the singular integral associated to the Cauchy kernel (or…

It is known that the classical Hilbert--Schmidt theorem can be generalized to the case of compact operators in Hilbert $A$-modules $H_A^*$ over a $W^*$-algebra of finite type, i.e. compact operators in $H_A^*$ under slight restrictions can…

A semiregular operator on a Hilbert C^*-module, or equivalently, on the C^*-algebra of `compact' operators on it, is a closable densely defined operator whose adjoint is also densely defined. It is shown that for operators on extensions of…

A classical problem in operator theory has been to determine the spectrum of Toeplitz-like operators on Hilbert spaces of vector-valued holomorphic functions on the open unit ball in C^m. In this note we obtain necessary conditions for…