Related papers: Left (right) pseudospectrum and left (right) condi…

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral…

In this article, we consider the linear operator equation in a Banach space. The relative perturbation of the solution x corresponding to the perturbation of y, the perturbation of A and the perturbation of both A, y are characterized from…

This paper deals with the condition pseudospectrum and essential condition pseudospectrum of operator pencils on n.a Banach spaces. We give a characterization of the condition pseudospectrum of operator pencils on n.a Banach spaces, the…

We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.

We prove several abstract results giving general conditions under which subspaces of linear or multilinear operators on Banach spaces or Banach lattices are closed. Each of these abstract results is followed by concrete applications,…

We prove the existence of the invariant subspaces of some operators in a real Banach space. For example, linear isometries have invariant subspaces

In this paper we give conditions under which sub differential limits can be better estimated.

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…

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…

We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…

Let $A$ be an unbounded operator on a Banach space $X$. It is sometimes useful to improve the operator $A$ by extending it to an operator $B$ on a larger Banach space $Y$ with smaller spectrum. It would be preferable to do this with some…

We establish the various properties as well as diverse relations of the ascent and descent spectra for bounded linear operators. We specially focus on the theory of subspectrum. Furthermore, we construct a new concept of convergence for…

In this paper, we define and study the pseudo upper and lower semi B-Fredholm of bounded operators in a Banach space. In particular, we prove equality up to $S(T)$ between the left generalized Drazin spectrum and the pseudo upper semi…

This article proposed a new approach to the determination of the spectrum for nonlinear continuous operators in the Banach spaces and using it investigated the spectrum of some classes of operators. Here shows that in nonlinear operators…

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…

Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a…

We consider the question of simultaneous extension of (pseudo)metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to K\"unzi and Shapiro for the case of extension…

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…

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…