Related papers: Representation theorems and variational principles…
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…
The two reference lists contain 54/22 references of papers and preprints concerned with the theory and/or various applications of Hilbert modules over Hilbert $*$-algebras and over (non-self-adjoint) operator algebras. They are far from…
Let $T$ be a $\delta$-Jordan Lie supertriple system. We first introduce the notions of generalized derivations and representations of $T$ and present some properties. Also, we study the low dimension cohomology and the coboundary operator…
The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the…
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…
The necessary and sufficient conditions for existence of a generalized representer theorem are presented for learning Hilbert space-valued functions. Representer theorems involving explicit basis functions and Reproducing Kernels are a…
We consider an arbitrary selfadjoint operator on a separable Hilbert space. To this operator we construct an expansion in generalized eigenfunctions in which the original Hilbert space is decomposed as a direct integral of Hilbert spaces…
We show that a class of dynamical systems induces an associated operator system in Hilbert space. The dynamical systems are defined from a fixed finite-to-one mapping in a compact metric space, and the induced operators form a covariant…
For finding the numerical solution of operator equations in many applications a decomposition in subspaces is needed. Therefore, it is necessary to extend the known method of matrix representation to the utilization of fusion frames. In…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…
This paper is a survey of our recent work on operator algebras associated to dynamical systems that lead to classification results for the systems in terms of algebraic invariants of the operator algebras.
In this work, firstly all normal extensions of a multipoint minimal operator generated by linear multipoint diferential-operator expression for first order in the Hilbert space of vector functions in terms of boundary values at the…
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a…
We show that, under certain regularity assumptions, there exists a linear extension operator.
We introduce a class of bipartite operators acting on $\mathcal{H} \otimes \mathcal{H}$ ($\mathcal{H}$ being an $n$-dimensional Hilbert space) defined by a set of $n$ Completely Different Permutations CDP. Bipartite operators are of…
We study several classes of indecomposable representations of quivers on infinite-dimensional Hilbert spaces and their relation. Many examples are constructed using strongly irreducible operators. Some problems in operator theory are…
We give an explicit correspondence between the domains of the self-adjoint extensions of a one-dimensional Schr\"odinger differential operator with symmetric real-valued potential and the boundary conditions the functions in the resulting…
In this paper, we will consider matrices with entries in the space of operators $\mathcal{B}(H)$, where $H$ is a separable Hilbert space, and consider the class of (left or right) Schur multipliers that can be approached in the multiplier…