Let be a C∗-algebra with identity 1, and let s( ) denote the set of all states on . For p,q,r ∈ [1,∞), denote by r( ) the set of all infinite matrices A= [ajk]j,k=1 over such that the matrix (φ[A[2]]) [r] := [(φ(ajkajk))]j,k=1 defines a bounded linear operator from p to q for all φ∈ s( ). Then r( ) is a Banach algebra with the Schur product operation and norm ‖A‖ = sup{‖(φ[A[2]])‖ : φ∈ s( )}. A...

Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of P...

Generalized scalar operators were introduced by C. Foia~ [4] and a detailed study of such operators can be found in the monograph [3]. An important subclass consists of regular generalized scalar operators which enjoy properties not shared by all generalized scalar operators. For example, the sum and product of commuting generalized scalar operators S and T need not be generalized scalar operat...

A self-adjoint operator A in a Krĕın space (K, [ · , · ]) is called partially fundamentally reducible if there exist a fundamental decomposition K = K+[+̇]K− (which does not reduce A) and densely defined symmetric operators S+ and S− in the Hilbert spaces (K+, [ · , · ]) and (K−,−[ · , · ]), respectively, such that each S+ and S− has defect numbers (1, 1) and the operator A is a self-adjoint ext...

The talk will summarize recent works on the stability under disorder of the absolutely continuous spectra of random operators on tree graphs. The cases covered include: Schroedinger operators with random potential, quantum graph operators for trees with randomized edge lengths, and Schroedinger operators with radial quasi-periodic potentials. The results were derived jointly with R. Sims and S....

One of the common strategies in the study of Toeplitz operators consists in selecting of various special symbol classes S ⊂ L∞ so that the properties of both the individual Toeplitz operators Ta, with a ∈ S, and of the algebra generated by such Toeplitz operators can be characterized. A motivation to study an algebra generated by Toeplitz operators (rather than just Toeplitz operators themselve...

Abstract. Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in t...