Related papers: Perturbation analysis for the linear operator equa…

Let $SS$ and $SC$ be the strictly singular and the strictly cosingular operators acting between Banach spaces, and let $P\Phi_+$ and $P\Phi_+$ be the perturbation classes for the upper and the lower semi-Fredholm operators. We study two…

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…

For an operator-differential equation of the form $y^{(m)}(z) = Ay(z)$, where $A$ is a closed linear operator on a Banach space over the the field of $p$-adic numbers, the necessary and sufficient conditions on initial data for the Cauchy…

We extend the Paley-Wiener pertubation theory to linear operators mapping a subspace of one Banach space into another Banach space.

In this paper, a sufficient condition for the existence of hyperinvariant subspace of compact perturbations of multiplication operators on some Banach spaces is presented. An interpretation of this result for compact perturbations of normal…

We discuss the problem of perturbation of spectral subspaces for linear self-adjoint operators on a separable Hilbert space. Let $A$ and $V$ be bounded self-adjoint operators. Assume that the spectrum of $A$ consists of two disjoint parts…

We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential…

In this paper we use abstract vector spaces and their duals without any canonical basis. Some of our results can be extended to infinite dimensional vector spaces too, but here we consider only finite dimensional spaces. We focus on a…

In this paper we study the Y-convexity, a property which is obtained by considering a real Banach sequence lattice Y instead of $\ell^p$ for a linear operator $T : E \rightarrow X$, where E is a Banach space and X is a Banach lattice. We…

Let $A,$ $T$ and $B$ be bounded linear operators on a Banach space. This paper is concerned mainly with finding some necessary and sufficient conditions for convergence in operator norm of the sequences $\left\{ A^{n}TB^{n}\right\} $ and…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…

In this paper, we establish a useful set of formulae for the $\sin\Theta$ distance between the original and the perturbed singular subspaces. These formulae explicitly show that how the perturbation of the original matrix propagates into…

This paper is concerned with inverse spectral problems for higher-order ($n > 2$) ordinary differential operators. We develop an approach to the reconstruction from the spectral data for a wide range of differential operators with either…

We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…

Let Z_0 be a bounded operator in a Banach space X with purely essential spectrum and K a nuclear operator in X. Using methods of complex analysis we study the discrete spectrum of Z_0+K and derive a Lieb-Thirring type inequality. We obtain…

This paper is concerned with the notions of admissibility, exact controllability, exact observability and regularity of linear systems in the Banach space setting. It is proved that admissible controllability, exact controllability,…

This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

A perturbational vector duality approach for objective functions $f\colon X\to \bar{L}^0$ is developed, where $X$ is a Banach space and $\bar{L}^0$ is the space of extended real valued functions on a measure space, which extends the…

We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…

The effect of matrix perturbations on the polar decomposition has been studied by several authors and various results are known. However, for operators between infinite-dimensional spaces the problem has not been considered so far. Here, we…