On the unconditional subsequence property
نویسندگان
چکیده
We show that a construction of Johnson, Maurey and Schechtman leads to the existence of a weakly null sequence (fi) in ( ∑ Lpi ) 2 , where pi ↓ 1, so that for all ε > 0 and 1 < q 2, every subsequence of (fi) admits a block basis (1+ ε)-equivalent to the Haar basis for Lq . We give an example of a reflexive Banach space having the unconditional subsequence property but not uniformly so. Published by Elsevier Inc.
منابع مشابه
On Quotients of Banach Spaces Having Shrinking Unconditional Bases
It is proved that if a Banach space Y is a quotient of a Banach space having a shrinking unconditional basis, then every normalized weakly null sequence in Y has an unconditional subsequence. The proof yields the corollary that every quotient of Schreier's space is c o-saturated. §0. Introduction. We shall say that a Banach space Y has property (WU) if every normalized weakly null sequence in Y...
متن کاملUnconditional Structures of Weakly Null Sequences
The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of c0, or there exists a subsequence which is boundedly convexly complete.
متن کاملPROPERTY ANALYSIS OF TRIPLE IMPLICATION METHOD FOR APPROXIMATE REASONING ON ATANASSOVS INTUITIONISTIC FUZZY SETS
Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...
متن کاملPre-compact Families of Finite Sets of Integers and Weakly Null Sequences in Banach Spaces
In this paper we provide a somewhat general framework for studying weakly null sequences in Banach spaces using Ramsey theory of families of finite subsets of N. Recall that the Ramsey theory on families of finite subsets of N was developed in a series of papers of Nash-Williams in the 60’s, a theory that is today naturally embedded in the more familiar infinite-dimensional Ramsey theory. The a...
متن کاملA Characterization of Subspaces and Quotients of Reflexive Banach Spaces with Unconditional Basis
We prove that the dual or any quotient of a separable reflexive Banach space with the unconditional tree property has the unconditional tree property. Then we prove that a separable reflexive Banach space with the unconditional tree property embeds into a reflexive Banach space with an unconditional basis. This solves several long standing open problems. In particular, it yields that a quotient...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009