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A new approach to the Ramsey-type games and the Gowers dichotomy in \(F\)-spaces. (English) Zbl 1274.46003

Summary: We give a new approach to the Ramsey-type results of Gowers on block bases in Banach spaces and apply our results to prove the Gowers dichotomy in \(F\)-spaces.

MSC:

46A16 Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)
46B15 Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces
91A05 2-person games
91A80 Applications of game theory
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References:

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