Unit:
Τομέας Μαθηματικής ΑνάλυσηςLibrary of the School of Science
Author:
Παναγάκου Βασιλική
Supervisors info:
Φαρμάκη Βασιλική Καθηγήτρια (Επιβλέπουσα), Παπαναστασίου Νικόλαος Επίκουρος καθηγητής, Τσαρπαλιάς Αθανάσιος Αναπληρωτής καθηγητής
Original Title:
Το διχοτομικό θεώρημα του T.Gowers για χώρους Banach
Summary:
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.
Keywords:
Gowers' dichotomy, unconditional basis, Banach spaces, Ramsey theory
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