Related papers: C*-module operators which satisfy in the generaliz…

Let $\mathcal H$ be an infinite-dimensional Hilbert space, and let $\mathcal B(\mathcal H)$ ($\mathcal K(\mathcal H)$) be the $C^*$-algebra of bounded (respectively, compact) linear operators in $\mathcal H$. Let $(E,\|\cdot\|_E)$ be a…

Given a C*-algebra A with a semicontinuous semifinite trace tau acting on the Hilbert space H, we define the family R of bounded Riemann measurable elements w.r.t. tau as a suitable closure, a la Dedekind, of A, in analogy with one of the…

For the class of Hardy spaces and standard weighted Bergman spaces of the unit disk we prove that the spectrum of a generalized Ces\`aro operator $T_g$ is unchanged if the symbol $g$ is perturbed to $g+h$ by an analytic function $h$…

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…

In this paper, we derive a generalized multiplicative Hardy-Littlewood-Polya type inequality, as well as several related additive inequalities, for functions of operators in Hilbert spaces. In addition, we find the modulus of continuity of…

Given C$^*$-algebras $A$ and $B$ acting cyclically on Hilbert spaces $\h$ and $\k$, respectively, we characterize completely isometric $A,B$-bimodule maps from $\bkh$ into operator $A,B$-bimodules. We determine cogenerators in some classes…

We give a short proof of the nuclearity property of a class of Cuntz-Pimsner algebras associated with a Hilbert A-bimodule M, where A is a separable and nuclear C*-algebra. We assume that the left A-action on the bimodule M is given in…

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…

Let $C^*(\cls)$ be the $C^*$ algebra generated by an operator system $\cls$ i.e. a unital $*$-closed subspace of a unital $C^*$ algebra $\cla$. We prove that any complete order isomorphism $\cli:\cls \raro \cls'$ between two such operator…

The following topics are presented in these notes: Elements of Banach algebras, Banach algebras of the form $L^1(G)$, where $G$ is a locally compact group, spectrum of elements of Banach algebras, the spectral theory of compact operators on…

We investigate structural properties and normality criteria for certain classes of bounded linear operators on a Hilbert space. We show that an operator $T$ with polar decomposition $T = U|T|$ is self-adjoint if and only if $T$ is…

We show that for a Hecke pair $(G, \Gamma)$ the $C^*$-completions $C^*(L^1(G, \Gamma))$ and $pC^*(\bar{G})p$ of its Hecke algebra coincide whenever the group algebra $L^1(\bar{G})$ satisfies a spectral property which we call…

In the paper, we prove an analogue of the Kato-Rosenblum theorem in a semifinite von Neumann algebra. Let $\mathcal{M}$ be a countably decomposable, properly infinite, semifinite von Neumann algebra acting on a Hilbert space $\mathcal{H}$…

Let $X$ be a right Hilbert module over a $C^*$-algebra $A$ equipped with the canonical operator space structure. We define an elementary operator on $X$ as a map $\phi : X \to X$ for which there exists a finite number of elements $u_i$ in…

Let $A$ be a non-zero positive bounded linear operator on a complex Hilbert space $(\mathcal{H},\langle\cdot,\cdot\rangle)$. Let $\omega_A(T)$ denote the $A$-numerical radius of an operator $T$ acting on the semi-Hilbert space…

Let $\mathscr E$ be a Hilbert $\mathscr A$-module over a $C^*$-algebra $\mathscr A$. For each positive linear functional $\omega$ on $\mathscr A$, we consider the localization $\mathscr E_\omega$ of $\mathscr E$, which is the completion of…

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the Cuntz-Nica-Pimsner algebra of X. Our construction…

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…

We provide a characterization for operator valued completely bounded linear maps on Hilbert $C^*$-modules in terms of $\varphi$-maps. Also, we show that for every operator valued completely positive map $\varphi$ on a $C^*$-algebra…

We introduce a product in all complex normed vector spaces, which generalizes the inner product of complex inner product spaces. Naturally the question occurs whether the Cauchy-Schwarz inequality is fulfilled. We provide a positive answer.…