Joint essential spectra

Stability of essential spectra of bounded linear operators

In this paper‎, ‎we show the stability of Gustafson‎, ‎Weidmann‎, ‎Kato‎, ‎Wolf‎, ‎Schechter and Browder essential spectrum of bounded linear operators on Banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $U$ such $gamma(U^m)

Computing Absolute and Essential Spectra Using Continuation

A continuation approach to the computation of essential and absolute spectra of reaction-diffusion operators on the real line is presented. The advantage of this approach compared with direct eigenvalue computations for the discretized operator are the efficient and accurate computation of selected parts of the spectrum (typically those near the imaginary axis) and the option to compute nonline...

Essential Spectra of Elliptic Partial Differential Equations

Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b) R(A —X), the range of A —X, is closed (c)...

Joint Browder Spectra and Tensor Products

Joint Spectra of Generators in Topological Algebras

Let be a complex topological algebra with unit 1 and a family of proper closed ideals in . For an arbitrary S⊂ we define a globally defined joint spectrum σ (S)= {(λs)s∈S ∈ CS |∃ I ∈ (s− λs) ∈ I ∀s ∈ S}. We prove that for S generating the spectrum σ (S) can be identified with the setM of continuous multiplicative functionals f on such that ker f ∈ . The relation is given by the formula σ (S)= {...