Related papers: Topological radicals, III. Joint spectral radius
We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient…
It is shown that the joint spectral radius $\rho(M)$ of a precompact family $M$ of operators on a Banach space $X$ is equal to the maximum of two numbers: the joint spectral radius $\rho_{e}(M)$ of the image of $M$ in the Calkin algebra and…
We develop the spectral radius technique and the theory of tensor radicals. As applications we obtain numerous results on mutiplication operators in Banach algebras and Operator bimodules.
We develop the theory of topological radicals in Banach Lie algebras, consider various ways of constructing such radicals and study a family of (pre)radicals related to subalgebras and ideals of finite codimension in Banach Lie algebras. It…
The work starts a series of papers on topological radicals and their applications. Among other results we present a theory of radicals related to the joint tensor radius.
We introduce the concept of topological radical of a Banach module. This closed submodule have two description: the as the intersection of ranges of maximal contractive monomorphism (from outside) and as the union of ranges of small…
The paper develops the theory of topological radicals of Banach Lie algebras and studies the structure of Banach Lie algebras with sufficiently many Lie subalgebras of finite codimensions -- the intersection of all these subalgebras is…
In this paper we discuss the infinite-dimensional generalizations of the famous theorem of Berger-Wang (generalized Berger-Wang formulas) and give an operator-theoretic proof of I. Morris's theorem about coincidence of three essential joint…
Let N be a nest on a Hilbert space H and AlgN the corresponding nest algebra. We determine the hypocompact radical of AlgN . Other topological radicals are also characterized.
Given the norms of powers $(\lVert x^n\rVert)_{n\geq 0}$ of a Banach algebra element $x$, the largest possible value of the minimum modulus on the spectrum of $x$ is determined. It is also shown that, given a Banach algebra element $x$ and…
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…
In this paper we study the joint/generalized spectral radius of a finite set of matrices in terms of its rank-one approximation by singular value decomposition. In the first part of the paper, we show that any finite set of matrices with at…
The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.
We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger-Wang's formula when restricted to the space of cocycles taking values in the space of compact operators.…
Generalizing the notion of numerical range and numerical radius of an operator on a Banach space, we introduce the notion of joint numerical range and joint numerical radius of tuple of operators on a Banach space. We study the convexity of…
It is a well-known fact in K-theory that the rapidly decreasing matrices of countable size form an associative topological algebra whose set of quasi-invertible elements is open, and such that the quasi-inversion map is continuous. We…
In this article, we extend several relation-theoretic notions to topological spaces. We introduce relation preserving contraction mapping into topological spaces and utilize the same to extend Banach contraction principle in topological…
Suppose $\mathcal{Z}$ is the space of all tuples of operators on a finite-dimensional Banach space endowed with the joint numerical radius norm. We obtain the structure of the extreme points of the dual unit ball of $\mathcal{Z}.$ Using…
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is…
We determine the local spectrum of a central element of the complexified universal enveloping algebra of a compact connected Lie group at a smooth function as an element of L^p(G). Based on this result we establish a corresponding local…