Ergodic Theorems and the Jacobs-deLeeuw-Glicksberg Decomposition

Beschreibung

For contractions on reflexive Banach spaces, the splitting theorem of Jacobs, deLeeuw and Glicksberg still yields a reduction to two invariant subspaces similar to the one obtained in the Hilbert space case. There is however no Banach space analogue of the van der Corput inequality, leaving the polynomial convergence open in the general Banach space case. Our aim in this thesis is threefold. We wish to obtain new and stronger characterisations of Hs, as it is the lesser understood of the two subspaces arising in the splitting. Second, we wish to apply the splitting results to investigate the existence of the limit of polynomial and entangled sequences and their properties. Finally we seek to obtain splitting results in the context of W algebras for more general semigroups, using the additional algebraic structure.
For contractions on reflexive Banach spaces, the splitting theorem of Jacobs, deLeeuw and Glicksberg still yields a reduction to two invariant subspaces similar to the one obtained in the Hilbert space case. There is however no Banach space analogue of the van der Corput inequality, leaving the polynomial convergence open in the general Banach space case. Our aim in this thesis is threefold. We wish to obtain new and stronger characterisations of Hs, as it is the lesser understood of the two subspaces arising in the splitting. Second, we wish to apply the splitting results to investigate the existence of the limit of polynomial and entangled sequences and their properties. Finally we seek to obtain splitting results in the context of W algebras for more general semigroups, using the additional algebraic structure.

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Dávid Kunszenti-Kovács

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