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• # Artykuł - szczegóły

## Studia Mathematica

2001 | 144 | 2 | 169-179

## Quasi-constricted linear operators on Banach spaces

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.

169-179

wydano
2001

### Twórcy

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