On the Multiplicity of an Analytic Operator-Valued Function.
On the problem of invariance under holomorphic functions for a set of continuity points of the spectrum function
On the spectral properties of tensor products of linear operators in Banach spaces
On the Taylor functional calculus
We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.
Operator means, fixed points, and the norm convergence of monotone approximants.
Operator theoretic properties of semigroups in terms of their generators
Let be a C₀ semigroup with generator A on a Banach space X and let be an operator ideal, e.g. the class of compact, Hilbert-Schmidt or trace class operators. We show that the resolvent R(λ,A) of A belongs to if and only if the integrated semigroup belongs to . For analytic semigroups, implies , and in this case we give precise estimates for the growth of the -norm of (e.g. the trace of ) in terms of the resolvent growth and the imbedding D(A) ↪ X.
Perturbations of the H∞-calculus
Suppose A is a sectorial operator on a Banach space X, which admits an H∞-calculus. We study conditions on a multiplicative perturbation B of A which ensure that B also has an H∞-calculus. We identify a class of bounded operators T : X→X, which we call strongly triangular, such that if B = (1 + T) A is sectorial then it also has an H∞-calculus. In the case X is a Hilbert space an operator is strongly triangular if and only if ∑ Sn(T)/n <∞ where (Sn(T))n=1∞ are the singular values of T.
Pick-Julia Theorems for Operators.
Polynomially bounded operators.
Power-bounded elements and radical Banach algebras
Firstly, we give extensions of results of Gelfand, Esterle and Katznelson--Tzafriri on power-bounded operators. Secondly, some results and questions relating to power-bounded elements in the unitization of a commutative radical Banach algebra are discussed.
Projektoren und relative Inversion holomorpher Semi-Fredholmfunktionen.
Properties and applications of the local functional calculus.
Propriétés analytiques des valeurs et vecteurs propres des opérateurs de l'espace de Hilbert
Propriétés spectrales des restrictions d’opérateurs de la classe
Puissances d'un opérateur régularisant
Quasispectra of solvable Lie algebra homomorphisms into Banach algebras
We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.
Randomly Weighted Series of Contractions in Hilbert Spaces.
Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators.
Relative Inverses of Meromorphic Operator Functions and Associated Holomorphic Projection Function.
Remarks on Kato's square-root problem.