Το διχοτομικό θεώρημα του T.Gowers για χώρους Banach

Φαρμάκη Βασιλική Καθηγήτρια (Επιβλέπουσα), Παπαναστασίου Νικόλαος Επίκουρος καθηγητής, Τσαρπαλιάς Αθανάσιος Αναπληρωτής καθηγητής

Το διχοτομικό θεώρημα του T.Gowers για χώρους Banach

In this Master Thesis we present Gowers' dichotomy theorem for Banach spaces. According to this theorem, a Banach space X has a subspace Y which either has unconditional basis or is hereditarily indecomposable. We present the proof of this basic theorem in three different ways. We start with the proof from Gowers' paper through a combinatorial Ramsey partition theorem for Banach spaces defining the Gowers' game for Banach spaces. Then we refer an equivalent game defined by Bagaria and Abad. Also, we give a direct proof of the basic dichotomy theorem by Maurey. Finally, we present an extension of Gowers' dichotomy theorem proved by Farmaki through a Ramsey partition theorem for Banach spaces for every countable ordinal.

XIV,66

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