Related papers: Spectral cuts and unconventional functional calcul…
We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of…
Let $X$ and $Y$ be separable Banach spaces and $T:X\to Y$ be a bounded linear operator. We characterize the non-separability of $T^*(Y^*)$ by means of fixing properties of the operator $T$.
Famous results due to von Neumann, Sz.-Nagy and Arveson assert that the following four statements are equivalent; a Hilbert space operator $T$ is a contraction; the closed unit disk $\overline{\mathbb D}$ is a spectral set for $T$; $T$ can…
We establish a spectral duality for certain unbounded operators in Hilbert space. The class of operators includes discrete graph Laplacians arising from infinite weighted graphs. The problem in this context is to establish a practical…
We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with…
The foundation of spectral theory on the $S$-spectrum can be traced back to the quaternionic framework of quantum mechanics. The concept of $S$-spectrum for quaternionic operators emerged as the natural spectrum in slice hyperholomorphic…
Let ${\mathcal B}(H)$ denote the Banach algebra of all bounded linear operators on a complex Hilbert space $H$ with $\dim H\geq 3$, and let $\mathcal A$ and $\mathcal B$ be subsets of ${\mathcal B}(H)$ which contain all rank one operators.…
The theory of quaternionic operators has applications in several different fields such as quantum mechanics, fractional evolution problems, and quaternionic Schur analysis, just to name a few. The main difference between complex and…
In this paper the general spectral properties of linear operators in Banach spaces are studied. We find sufficient conditions on structure of Banach spaces and resolvent properties that guarantee completeness of roots elements of Schatten…
Real linear operators between two complex Banach spaces unify naturally two important classes of linear operators and antilinear operators. We give a survey of basic geometric, spectral and duality properties of real linear operators. The…
We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to…
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…
Given a complex Banach space $X$ and a joint spectrum for complex solvable finite dimensional Lie algebras of operators defined on $X$, we extend this joint spectrum to quasi-solvable Lie algebras of operators, and we prove the main…
There has been a long-standing conjecture in Banach algebra that every amenable operator is similar to a normal operator. In this paper, we study the structure of amenable operators on Hilbert spaces. At first, we show that the conjecture…
In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…
The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…
A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic if there is a subspace $M \subsetneq X$ and a vector $x \in X$ such that $orb{(x,T)} \cap M$ is dense in $M$. We show that every Banach space supports…
It is shown that if the Deddens algebra ${\mathcal D}_T$ associated with a quasinilpotent operator $T$ on a complex Banach space is closed and localizing then $T$ has a nontrivial closed hyperinvariant subspace.
The classical Perron-Frobenius theory asserts that an irreducible matrix $A$ has cyclic peripheral spectrum and its spectral radius $r(A)$ is an eigenvalue corresponding to a positive eigenvector. In Radjavi (1999) and Radjavi and Rosenthal…
In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…