Classical results of Pelczynski and of Zippin concerning bases in Banach spaces are extended to the Fréchet space setting; thus answering to a question posed by Kalton almost 40 years ago. Equipped with these results, we prove that a Fréchet space with a basis is reflexive (resp. Montel) if and only if every power bounded operator is mean ergodic (resp. uniformly ergodic). New techniques are developed and many examples in classical Fréchet spaces are exhibited.
Mean Ergodic operators in Fréchet spaces
ALBANESE, Angela Anna;
2009-01-01
Abstract
Classical results of Pelczynski and of Zippin concerning bases in Banach spaces are extended to the Fréchet space setting; thus answering to a question posed by Kalton almost 40 years ago. Equipped with these results, we prove that a Fréchet space with a basis is reflexive (resp. Montel) if and only if every power bounded operator is mean ergodic (resp. uniformly ergodic). New techniques are developed and many examples in classical Fréchet spaces are exhibited.File in questo prodotto:
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