Related papers: On compressions and generalized spectra of operato…

In this paper, we extend Fredholm theory in von Neumann algebras established by Breuer in [5] and [6] to spectral Fredholm theory. We consider 2 by 2 upper triangular operator matrices with coefficients in a von Neumann algebra and give the…

In this paper, we introduce the notion of invariant submodule in the theory of Hilbert C*-modules and study some basic properties of bounded adjointable operators and their generalized inverses which have nontrivial invariant submodules. We…

After recalling in detail some basic definitions on Hilbert C*-bimodules, Morita equivalence and imprimitivity, we discuss a spectral reconstruction theorem for imprimitivity Hilbert C*-bimodules over commutative unital C*-algebras and…

We consider problems associated with the computation of spectra of self-adjoint operators in terms of the eigenvalue distributions of their n x n sections. Under rather general circumstances, we show how these eigenvalues accumulate near…

We obtain some results about the spectrum and the upper semi-Fredholm spectrum of weighted composition operators on uniform algebras, assuming that the corresponding map maps the Shilov boundary onto itself. In particular, it follows from…

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…

Given an essential ideal $J\subset A$ of a C*-algebra $A$, and a Hilbert C*-module $M$ over $A$, we place $M$ between two other Hilbert C*-modules over $A$, $M_J\subset M\subset M^J$, in such a way that each submodule here is thick, i.e.…

The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…

We treat spectral problems by twisted groupoid methods. To Hausdorff locally compact groupoids endowed with a continuous $2$-cocycle one associates the reduced twisted groupoid $C^*$-algebra. Elements (or multipliers) of this algebra admit…

The study of operator algebras on Hilbert spaces, and C*-algebras in particular, is one of the most active areas within Functional Analysis. A natural generalization of these is to replace Hilbert spaces (which are $L^2$-spaces) with…

We consider projectivity and injectivity of Hilbert C*-modules in the categories of Hilbert C*-(bi-)modules over a fixed C*-algebra of coefficients (and another fixed C*-algebra represented as bounded module operators) and bounded…

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…

We study bounded operators defined in terms of the regular representations of the $C^*$-algebra of an amenable, Hausdorff, second countable locally compact groupoid endowed with a continuous $2$-cocycle. We concentrate on spectral…

We characterize lower semi-Fredholm and Fredholm of weighted composition operators on $C(K)$ in the case when the corresponding map is an open surjection of the compact space $K$ onto itself. The obtained criterions involve the notion of…

We extend the spectral theory of commutative C*-categories to the non full-case, introducing a suitable notion of spectral spaceoid provinding a duality between a category of "non-trivial" *-functors of non-full commutative C*-categories…

We study the essential spectrum and Fredholm properties of integral and pseudodiferential operators associated to (maybe non-commutative) locally compact groups G. The techniques involve crossed product C*-algebras. We extend previous…

We say that a contractive Hilbert space operator is universal if there is a natural surjection from its generated C*-algebra to the C*-algebra generated by any other contraction. A universal contraction may be irreducible or a direct sum of…

Let E be an operator algebra on a Hilbert space with finite-dimensional generated C*-algebra. A classification is given of the locally finite algebras and the operator algebras obtained as limits of direct sums of matrix algebras over E…

we show that the definitions of some classes of semi-Fredholm operators, which use the language of algebra and first introduced by X. Fang in [8], are equivalent to that of some well-known operator classes. For example, the concept of…

Let $G=K\ltimes A$ be the semi-direct product group of a compact group $K$ acting on an abelian locally compact group $A$. We describe the $C^*$-algebra $C^*(G)$ of $G$ in terms of an algebra of operator fields defined over the spectrum of…