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Ascent spectrum and essential ascent spectrum

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Fredj O., Burgos M., Oudghiri M.

Studia Mathematica

2008

tom 187

nr 1

59-73

We study the essential ascent and the related essential ascent spectrum of an operator on a Banach space. We show that a Banach space X has finite dimension if and only if the essential ascent of every operator on X is finite. We also focus on the stability of the essential ascent spectrum under perturbations, and we prove that an operator F on X has some finite rank power if and only if $σ_{asc}^{e}(T + F) = σ_{asc}^{e}(T)$ for every operator T commuting with F. The quasi-nilpotent part, the analytic core and the single-valued extension property are also analyzed for operators with finite essential ascent.

Ograniczanie wyników

1 Studia Mathematica

1 Burgos M.

1 Fredj O.

1 Oudghiri M.

1 2008

Wyniki wyszukiwania

Ascent spectrum and essential ascent spectrum