Unconditional structures of weakly null sequences
نویسندگان
چکیده
منابع مشابه
Unconditional 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 کاملWeakly Null Sequences in L1
In [MR], the second author and H. P. Rosenthal constructed the first examples of weakly null normalized sequences which do not have any unconditionally basic subsequences. Much more recently, the second author and W. T. Gowers [GM] constructed infinite dimensional Banach spaces which do not contain any unconditionally basic sequences. These later examples are of a different character than the e...
متن کاملPartial unconditionality of weakly null sequences
We survey a combinatorial framework for studying subsequences of a given sequence in a Banach space, with particular emphasis on weakly-null sequences. We base our presentation on the crucial notion of barrier introduced long time ago by Nash-Williams. In fact, one of the purposes of this survey is to isolate the importance of studying mappings defined on barriers as a crucial step towards solv...
متن کاملWeakly null sequences with upper lp-estimates
A Banach space X has property (S) if every weakly null sequence in BaX, the unit ball of X, has a subsequence which is C-dominated by the unit vector basis of c0 for some constant C < ∞. In [11] it was shown that if X has property (S), then the constant C can be chosen to be independent of the particular weakly null sequence in BaX. Here we generalize this result to the case of upper lp-estimates.
متن کاملWeakly Null Sequences with Upper Estimates
Abstract. We prove that if (vi) is a normalized basic sequence and X is a Banach space such that every normalized weakly null sequence in X has a subsequence that is dominated by (vi), then there exists a uniform constant C ≥ 1 such that every normalized weakly null sequence in X has a subsequence that is C-dominated by (vi). This extends a result of Knaust and Odell, who proved this for the ca...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2001
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-01-02711-8