Related papers: Bistochastic operators and quantum random variable…

We introduce an operator valued Short-Time Fourier Transform for certain classes of operators with operator windows, and show that the transform acts in an analogous way to the Short-Time Fourier Transform for functions, in particular…

We introduce a localization concept for operator-valued frames, where the quality of localization is measured by the associated operator-valued Gram matrix belonging to some suitable Banach algebra. We prove that intrinsic localization of…

We consider linear operators defined on a subspace of a complex Banach space into its topological antidual acting positively in a natural sense. The goal of this paper is to investigate of this kind of operators. The main theorem is a…

Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…

We give orthonormal characterizations of collectively compact (limited) sets of linear operators from a Hilbert space to a Banach space.

The manifold structure of subsets of classical probability distributions and quantum density operators in infinite dimensions is investigated in the context of $C^{*}$-algebras and actions of Banach-Lie groups. Specificaly, classical…

Let ${\Bbb G}$ be a locally compact quantum group and ${\mathcal T}(L^2({\Bbb G}))$ be the Banach algebra of trace class operators on $L^2({\Bbb G})$ with the convolution induced by the right fundamental unitary of ${\Bbb G}$. We study the…

We consider Fourier transform of vector-valued functions on a locally compact group $G$, which take value in a Banach space $X$, and are square-integrable in Bochner sense. If $G$ is a finite group then Fourier transform is a bounded…

Let $\mu$ be a positive Borel measure on $[0,1)$. If $f \in H(\mathbb{D})$ and $\alpha>-1$, the generalized integral type Hilbert operator defined as follows: $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int^1_{0}…

Let $X$ be a Borel metric measure space such that each closed ball is of positive and finite measure. In this paper, we give a sufficient and necessary condition for averaging operators on a Banach function space $E(X)$ on $X$ to be…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

Based on the operator representation on the module over Banach algebra $B(X)$, the Campbell-Baker-Hausdorff formula is generalized to the unbounded situations. In conclusion, by means of the logarithmic representation of generally-unbounded…

A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…

In this paper, we investigate the boundedness of composition operators defined on a quasi-Banach space continuously included in the space of smooth functions on a manifold. We prove that the boundedness of a composition operator strongly…

We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…

A Wiener-Hopf operator on a Banach space of functions on R+ is a bounded operator T such that P^+S_{-a}TS_a=T, for every positive a, where S_a is the operator of translation by a. We obtain a representation theorem for the Wiener-Hopf…

We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely…

Let ${\mathcal B}(H)$ denote the Banach algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 3$, and let $\mathcal A$ and $\mathcal B$ be subsets of ${\mathcal B}(H)$ which contain all rank one operators.…

On finite dimensional spaces, it is apparent that an operator is the product of two positive operators if and only if it is similar to a positive operator. Here, the class ${\mathcal L}^{+2}$ of bounded operators on separable infinite…

We show that a bounded quasinilpotent operator $T$ acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator $F$ and a scalar $\alpha\in\mathbb{C}$, $\alpha\neq 0$, $\alpha\neq…