Quasi-constricted linear operators on Banach spaces

• Autorzy: Eduard Yu. Emel'yanov , Manfred P. H. Wolff
• Języki publikacji: EN

Abstrakty

EN

Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace $X₀: = {x ∈ X: lim_{n→ ∞} ||Tⁿx|| = 0}$ is closed and has finite codimension. We show that a power bounded linear operator T ∈ L(X) is quasi-constricted iff it has an attractor A with Hausdorff measure of noncompactness $χ_{||·||₁}(A) < 1$ for some equivalent norm ||·||₁ on X. Moreover, we characterize the essential spectral radius of an arbitrary bounded operator T by quasi-constrictedness of scalar multiples of T. Finally, we prove that every quasi-constricted operator T such that λ̅T is mean ergodic for all λ in the peripheral spectrum $σ_{π}(T)$ of T is constricted and power bounded, and hence has a compact attractor.

Kategorie tematyczne

• 47A65: Structure theory
• 47A35: Ergodic theory
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 144
• Numer: 2
• Strony: 169-179

Daty

wydano

2001

Twórcy

autor

Eduard Yu. Emel'yanov

• Sobolev Institute of Mathematics at Novosibirsk, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia
• Mathematisches Institut der, Universität Tübingen, A. D. Morgenstelle 2, D-72076 Tübingen, Germany

autor

Manfred P. H. Wolff

• Mathematisches Institut der Universität Tübingen, A. D. Morgenstelle 2, D-72076 Tübingen, Germany

Identyfikatory

DOI

10.4064/sm144-2-5