Related papers: On The Absolute Value of Unbounded Operators
Given an infinite graph $G$ on countably many vertices, and a closed, infinite set $\Lambda$ of real numbers, we prove the existence of an unbounded self-adjoint operator whose graph is $G$ and whose spectrum is $\Lambda$.
Frames and orthonormal bases are naturally linked to bounded operators. To tackle unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also…
In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.
General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are…
In this paper, we investigate the algebras of consequence operators and finite consequence operators on a fixed language. Significant new collections of consequence operators are defined and shown to be complete and distributive…
In this paper we define the deficiency indices of a closed symmetric right $\mathbb{H}$-linear operator and formulate a general theory of deficiency indices in a right quaternionic Hilbert space. This study provides a necessary and…
The necessity of a Maximum Principle arises naturally when one is interested in the study of qualitative properties of solutions to partial differential equations. In general, to ensure the validity of these kind of principles one has to…
We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its…
Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition…
Among other results we investigate $\left( \alpha,\beta\right) $-lineability of the set of non-continuous $m$-linear operators defined between normed spaces as a subset of the space of all $m$-linear operators. We also give a partial answer…
We establish a bijection between the self-adjoint extensions of the Laplace operator on a bounded regular domain and the unitary operators on the boundary. Each unitary encodes a specific relation between the boundary value of the function…
We give a self-contained and introductory account of some basic functional analytic tools needed to understand maximal monotone operators in Hilbert spaces. We review domains of (possibly unbounded) operators, closed sets and closed…
Let $\mathcal{L}(X;Y)$ be the space of bounded linear operators from a Banach space $X$ to a Banach space $Y$. Given an operator-valued function $u:\mathbb{R}_{\geq 0}\rightarrow \mathcal{L}(X;Y)$, suppose that every orbit $t\mapsto u(t)x$…
Several recent papers investigated unbounded convergences in Banach lattices. Combine all unbounded convergences, including unbounded order (norm, absolute weak, absolute weak*) convergence, we characterize L-weakly compact sets, L-weakly…
For a closed densely defined operator $T$ from a Hilbert space $\mathfrak{H}$ to a Hilbert space $\mathfrak{K}$, necessary and sufficient conditions are established for the factorization of $T$ with a bounded nonnegative operator $X$ on…
We investigate the $R$-boundedness of parameter-dependent families of Poisson operators on the half-space $\mathbb R^n_+$ in various scales of function spaces. Applications concern maximal $L_q$-regularity for boundary value problems with…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
Given self-adjoint operators $A, B\in\mathbb{B}(\mathscr{H})$ it is said $A\leq_uB$ whenever $A\leq U^*BU$ for some unitary operator $U$. We show that $A\leq_u B$ if and only if $f(g(A)^r)\leq_uf(g(B)^r)$ for any increasing operator convex…
The present paper partly constitutes an "unbounded" follow-up of a paper by I. Kaplansky dealing with bounded products of normal operators. Results on the normality of unbounded products are also included.
We establish necessary and sufficient conditions for boundedness of composition operators on the most general class of Hilbert spaces of entire Dirichlet series with real frequencies. Depending on whether or not the space contains any…