We characterize tauberian operators $T:L_1\left(\mu \right)\to Y$ in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in $L_1[0,1]$. As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator $T:L_1\left(\mu \right)\to Y$ is also tauberian, and the induced operator $T̃:L_1\left(\mu \right)**/L_1\left(\mu \right)\to Y**/Y$ is an isomorphism into. Also, we show that $L_1\left(\mu \right)$ embeds...

Let X be a Banach space and $f\in L_l^{1}oc(ℝ;X)$ be absolutely regular (i.e. integrable when divided by some polynomial). If the distributional Fourier transform of f is locally integrable then f converges to 0 at infinity in some sense to be made precise. From this result we deduce some Tauberian theorems for Fourier and Laplace transforms, which can be improved if the underlying Banach space has the analytic Radon-Nikodym property.

2000 Mathematics Subject Classification: 47A10, 47A13.In this paper, we give a description of Taylor spectrum of commuting 2-contractions in terms of characteritic functions of such contractions. The case of a single contraction obtained by B. Sz. Nagy and C. Foias is generalied in this work.

A Banach space operator T ∈ has a left m-inverse (resp., an essential left m-inverse) for some integer m ≥ 1 if there exists an operator S ∈ (resp., an operator S ∈ and a compact operator K ∈ ) such that ${\sum }_{i=0}^m{(-1)}^i\left(\genfrac{}{}{0pt}{}{m}{i}\right)S^{m-i}{T}^{m-i}=0$ (resp., ${\sum }_{i=0}^m{(-1)}^i\left(\genfrac{}{}{0pt}{}{m}{i}\right)T^{m-i}{S}^{m-i}=K$). If $T_i$ is left $m_i$-invertible (resp., essentially left $m_i$-invertible), then the tensor product T₁ ⊗ T₂ is left (m₁ + m₂-1)-invertible (resp., essentially left (m₁ + m₂-1)-invertible). Furthermore, if T₁ is strictly left m-invertible (resp., strictly essentially left m-invertible), then...

Mediante l'uso della teoria dei problemi intermedi vengono dati metodi di calcolo per gli operatori di Green e per le relative funzioni di Green di problemi del tipo: data $f\in S$, determinare $u\in H$ tale che ${\left(Tu,v\right)}_H={\left(f,v\right)}_S$, $\mathrm{\forall }v\in H$, dove $S$ ed $H$ sono spazi di Hilbert, $H\subset S$, $T$ è un operatore lineare da $H$ in $H$ che verifica opportune ipotesi. Si ottengono maggiorazioni esplicite «a priori», tanto prossime a quella ottimale quanto si vuole.

We study the relations between simetrization by a limiting process of probabilities and functions defined on a metric compacy product space and their ergodic properties.

We present a model for two doubly commuting operator weighted shifts. We also investigate general pairs of operator weighted shifts. The above model generalizes the model for two doubly commuting shifts. WOT-closed algebras for such pairs are described. We also deal with reflexivity for such pairs assuming invertibility of operator weights and a condition on the joint point spectrum.

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pencil. In the second part of the paper we apply this result...