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Quasi-constricted linear operators on Banach spaces

Eduard Yu. Emel'yanov, Manfred P. H. Wolff (2001)

Studia Mathematica

Let X be a Banach space over ℂ. The bounded linear operator T on X is called quasi-constricted if the subspace X : = x X : l i m n | | T x | | = 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 | | · | | ( 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...

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