Related papers: Classification of irreversible and reversible Pims…
Devinatz, Nussbaum and von Neumann established some important results on the strong commutativity of self-adjoint and normal unbounded operators. In this paper, we prove results in the same spirit.
Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…
With the aim of completing the previous study by A. Or{\l}owski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter…
In this paper, we first introduce the notion of a (relative) averaging operator of any nonzero weight $\lambda$. We show that such operators are intimately related to triassociative algebras introduced by Loday and Ronco. Next, we construct…
For a long time, practitioners of the art of operator algebras always worked over the complex numbers, and nobody paid much attention to real C*-algebras. Over the last thirty years, that situation has changed, and it's become apparent that…
In this paper, we introduce the concepts of endomorphism operator, left averaging operator, differential operator and Rota-Baxter Operator, and we construct examples of these linear maps on associative algebras with a left identity, a…
In this paper we survey our recent work on C*-correspondences and their associated operator algebras; in particular, on adding tails, the Shift Equivalence Problem and Hilbert bimodules.
The present paper presents a survey of some recent results devoted to derivations, local derivations and 2-local derivations on various algebras of measurable operators affiliated with von Neumann algebras. We give a complete description of…
For 0 < s < 1, let phi_s(z)=sz+(1-s). We investigate the unital C*-algebra generated by the semigroup {C_{phi_s} : 0 < s < 1} of composition operators acting on the Hardy space of the unit disk. We determine the joint approximate point…
This note presents an analysis of a class of operator algebras constructed as cross-sectional algebras of flat holomorphic matrix bundles over a finitely bordered Riemann surface. These algebras are partly inspired by the bundle shifts of…
We study adjointable, bounded operators on the direct sum of two copies of the standard Hilbert C*-module over a unital C*-algebra A that are given by upper triangular 2 by 2 operator matrices. Using the definition of A-Fredholm and…
For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the…
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…
Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an…
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…
Let $\sS$ be a countable, abelian semigroup of continuous surjections on a compact metric space $X$. Corresponding to this dynamical system we associate two operator algebras, the tensor algebra, and the semicrossed product. There is a…
Given a directed graph, there exists a universal operator algebra and universal C*-algebra associated to the directed graph. In this paper we give intrinsic constructions of these objects. We provide an explicit construction for the maximal…
The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…
We investigate some new classes of operator algebras which we call semi-$\sigma$-finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson's…
A non-self-adjoint operator algebra is said to be residually finite dimensional (RFD) if it embeds into a product of matrix algebras. We characterize RFD operator algebras in terms of their matrix state space, and moreover show that an…