Related papers: Two classes of operators related to the perturbati…
We show that any bounded operator $T$ on a separable, reflexive, infinite-dimensional Banach space $X$ admits a rank one perturbation which has an invariant subspace of infinite dimension and codimension. In the non-reflexive spaces, we…
We consider the operators $H_0=M_0^{-1}(x) P(D)$ and $H =M^{-1} (x) P(D)$ where $M_0 (x)$ and $M (x)$ are positively definite bounded matrix-valued functions and $P(D)$ is an elliptic differential operator. Our main result is that the wave…
We investigate the duality and norm completeness in the classes of limitedly--L-weakly compact and Dunford--Pettis--L-weakly compact and operators from Banach spaces to Banach lattices.
We investigate the commutativity and semi-commutativity of generalized singular integral operators of the form $P_{+} f P_{+} + P_{-} g P_{+} + P_{+} u P_{-} + P_{-} v P_{-}$ on $L^{2}$, where $P_{+}$ denotes the Riesz projection and…
On the twisted Fock spaces $ \mathcal{F}^\lambda(\mathbb{C}^{2n}) $ we consider two types of convolution operators $ S_\varphi $ and $ \widetilde{S}_\varphi $ associated to an element $ \varphi \in \mathcal{F}^\lambda(\mathbb{C}^{2n}) .$ We…
The present contribution investigates shape optimisation problems for a class of semilinear elliptic variational inequalities with Neumann boundary conditions. Sensitivity estimates and material derivatives are firstly derived in an…
The purpose of the paper is to introduce and study a new class of operators on semi-Hilbertian spaces i.e.; spaces generated by positive semidefinite sesquilinear forms. Let H be a Hilbert space and let A be a positive bounded operator on H…
Global folds between Banach spaces are obtained from a simple geometric construction: a Fredholm operator $T$ of index zero with one dimensional kernel is perturbed by a compatible nonlinear term $P$. The scheme encapsulates most of the…
We prove the existence of a complex valued $C^2$-function on the unit circle, a unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class $S^2$, such that the perturbated operator $$ f(e^{iZ}U)-f(U)…
An operator $T \in \mathcal{B}(X)$ defined on a Banach space $X$ satisfies property $(gb)$ if the complement in the approximate point spectrum $\sigma_{a}(T)$ of the upper semi-B-Weyl spectrum $\sigma_{SBF_{+}^{-}}(T)$ coincides with the…
We consider the spectral Dirichlet problem for the Laplace operator in the plane $\Omega^{\circ}$ with double-periodic perforation but also in the domain $\Omega^{\bullet}$ with a semi-infinite foreign inclusion so that the Floquet-Bloch…
Motivated by a seminal paper of professor M. Z. Nashed published in 1987 on classification of ill-posed linear operator equations and distinguishing two types of ill-posedness in Banach and Hilbert spaces, we present, illustrate and justify…
In the paper is considered two problems on extension of operators whose range space for the first problem (or domain space for the second one) belongs to the fixed class of finite equivalence, which is generated by a given Banach space $X$.…
The algebra of Dirichlet series $\mathcal{A}(\mathcal{C}_{+})$ consists on those Dirichlet series convergent in the right half-plane $\mathcal{C}_{+}$ and which are also uniformly continuous there. This algebra was recently introduced by…
We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…
In this article we investigate the disjointly non-singular (DNS) operators. Following [8] we say that an operator $T$ from a Banach lattice $F$ into a Banach space $E$ is DNS, if no restriction of $T$ to a subspace generated by a disjoint…
Real and complex norms of a linear operator acting on a normed complexified space are considered. Bounds on the ratio of these norms are given. The real and complex norms are shown to coincide for four classes of operators: 1) real linear…
We study perturbations of functions $f(A,B)$ of noncommuting self-adjoint operators $A$ and $B$ that can be defined in terms of double operator integrals. We prove that if $f$ belongs to the Besov class $B_{\be,1}^1(\R^2)$, then we have the…
The importance of the theory of pseudo-differential operators in the study of non linear integrable systems is point out. Principally, the algebra $\Xi $ of nonlinear (local and nonlocal) differential operators, acting on the ring of…
We generalize our results of \cite{AP2} and \cite{AP3} to the case of maximal dissipative operators. We obtain sharp conditions on a function analytic in the upper half-plane to be operator Lipschitz. We also show that a H\"older function…