Some Version of Gowers’ Dichotomy for Banach Spaces
نویسنده
چکیده
In this paper another version of Gowers’ dichotomy for Banach spaces, involving topologies of special type on the Cartesian product of Banach spaces, is presented. These topologies are closely related to the game used by W. T. Gowers in his proof of the dichotomy.
منابع مشابه
An infinite Ramsey theorem and some Banach - space dichotomies
A problem of Banach asks whether every infinite-dimensional Banach space which is isomorphic to all its infinite-dimensional subspaces must be isomorphic to a separable Hilbert space. In this paper we prove a result of a Ramsey-theoretic nature which implies an interesting dichotomy for subspaces of Banach spaces. Combined with a result of Komorowski and TomczakJaegermann, this gives a positive...
متن کاملA new approach to the Ramsey-type games and the Gowers dichotomy in F-spaces
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.
متن کاملΑ-minimal Banach Spaces
A Banach space W with a Schauder basis is said to be α-minimal for some α < ω1 if, for any two block subspaces Z,Y ⊆ W, the Bourgain embeddability index of Z into Y is at least α. We prove a dichotomy that characterises when a Banach space has an αminimal subspace, which contributes to the ongoing project, initiated by W. T. Gowers, of classifying separable Banach spaces by identifying characte...
متن کاملCoding into Ramsey Sets
In [6] W. T. Gowers formulated and proved a Ramseytype result which lies at the heart of his famous dichotomy for Banach spaces. He defines the notion of weakly Ramsey set of block sequences of an infinite dimensional Banach space and shows that every analytic set of block sequences is weakly Ramsey. We show here that Gowers’ result follows quite directly from the fact that all Gδ sets are weak...
متن کاملAsymptotic L P Spaces and Bounded Distortions
The new class of Banach spaces, so-called asymptotic lp spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm. 0 Introduction During the last year several problems ...
متن کامل