Related papers: Weak commutation relations of unbounded operators …
In infinite-dimensional Hilbert spaces, the application of the concept of quasi-Hermiticity to the description of non-Hermitian Hamiltonians with real spectra may lead to problems related to the definition of the metric operator. We discuss…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
We consider the structure of algebra of operators, acting in $n-$fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its…
In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type $$\int_{[0, 1]}(- \Delta)^s u d \mu(s),$$ for a signed measure $\mu$ on the interval of fractional…
Let $T$ and $V$ be two Hilbert space contractions and let $X$ be a linear bounded operator. It was proved by C. Foias and J.P. Williams that in certain cases the operator block matrix $R(X;T,V)$ (defined in the text) is similar to a…
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is…
We show how the notion of {\em pseudo-bosons}, originally introduced as operators acting on some Hilbert space, can be extended to a distributional settings. In doing so, we are able to construct a rather general framework to deal with…
In this paper we study subspaces which are invariant under squares and cubes (separately as well as jointly) of unicellular backward weighted shift operators on a separable Hilbert space. The finite-dimensional subspaces are characterized…
This paper explores the Invariant Subspace Problem in operator theory and functional analysis, examining its applications in various branches of mathematics and physics. The problem addresses the existence of invariant subspaces for bounded…
Different estimates for the norm of the self-commutator of a Hilbert space operator are proposed. Particularly, this norm is bounded from above by twice of the area of the numerical range of the operator. An isoperimetric-type inequality is…
In 2008, J. Parcet showed the $(1,1)$ weak-boundedness of Calder\'on-Zygmund operators acting on functions taking values in a von Neumann algebra. We propose a simplified version of his proof using the same tools : Cuculescu's projections…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…
We explicitly construct two classes of infinitly many commutative operators in terms of the deformed W-algebra $W_{qt}(sl_N^)$, and give proofs of the commutation relations of these operators. We call one of them local integrals of motion…
We define and discuss properties of the class of unbounded operators which attain minimum modulus. We establish a relationship between this class and the class of norm attaining bounded operators and compare the properties of both. Also we…
We give an explicit description of all minimal self-adjoint extensions of a densely defined, closed symmetric operator in a Hilbert space with deficiency indices $(1, 1)$.
Ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…