On the spectrum of a one-parameter strongly continous representation.
On the spectrum of multipliers in Bessel potential spaces
On the spectrum of singularly perturbed operators
On the spectrum of stochastic perturbations of the shift and Julia sets
We extend the Killeen-Taylor study [Nonlinearity 13 (2000)] by investigating in different Banach spaces (,c₀(ℕ),c(ℕ)) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in the Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectrum is related to the Julia set of an endomorphism of ℂ².
On the spectrum of the analytic generator.
On the spectrum of the operator which is a composition of integration and substitution
Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator be defined on L₂[0,1]. We prove that has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator always equals 1.
On the spectrum of -contracting operators.
On the Spherical Spectrum.
On the Steps of Convergence of Approximate Eigenvectors in the Rayleigh-Schrödinger Series.
On the structure of commuting isometries
On the structure of relative identification operators for quantum fields and their connection with the Haag-Ruelle scattering theory
On the structure of the wave operators in one dimensional potential scattering.
On the Surjective Dunford-Pettis Property.
On the surjective Dunford-Pettis property
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.
On the tensor product weakly compact operators.
On the topological boundary of the one-sided spectrum
It is well-known that the topological boundary of the spectrum of an operator is contained in the approximate point spectrum. We show that the one-sided version of this result is not true. This gives also a negative answer to a problem of Schmoeger.
On the two weights problem for the Hilbert transform.
In this paper, we prove sufficient conditions on pairs of weights (u,v) (scalar, matrix or operator valued) so that the Hilbert transform H f(x) = p.v. ∫ [f(y) / x - y] dy,is bounded from L2(u) to L2(v).
On the uniform ergodic theorem in Banach spaces that do not contain duals
Let T be a power-bounded linear operator in a real Banach space X. We study the equality (*) . For X separable, we show that if T satisfies and is not uniformly ergodic, then contains an isomorphic copy of an infinite-dimensional dual Banach space. Consequently, if X is separable and does not contain isomorphic copies of infinite-dimensional dual Banach spaces, then (*) is equivalent to uniform ergodicity. As an application, sufficient conditions for uniform ergodicity of irreducible Markov chains...
On the weak decomposition property
We study a new class of bounded linear operators which strictly contains the class of bounded linear operators with the decomposition property (δ) or the weak spectral decomposition property (weak-SDP). We treat general local spectral properties for operators in this class and compare them with the case of operators with (δ).