منابع مشابه
On weak compactness in L1 spaces
We will use the concept of strong generating and a simple renorming theorem to give new proofs to slight generalizations of some results of Argyros and Rosenthal on weakly compact sets in L1(μ) spaces for finite measures μ. The purpose of this note is to show that a simple transfer renorming theorem explains why L1(μ)-spaces, for finite measures μ, share some properties with superreflexive spac...
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One of the most important goals of set theorists over the last few years has been to re-prove old results which previously had used very strong assumptions from hypotheses which, at least prima facie, are weaker. Examples of these abound, including, but certainly not limited to, the work of Woodin and Cummings (see [3]) on the Singular Cardinals Problem, in which results previously obtained by ...
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We study the logical and computational strength of weak compactness in the separable Hilbert space `2. Let weak-BW be the statement the every bounded sequence in `2 has a weak cluster point. It is known that weak-BW is equivalent to ACA0 over RCA0 and thus that it is equivalent to (nested uses of) the usual Bolzano-Weierstraß principle BW. We show that weak-BW is instance-wise equivalent to Π2-...
متن کاملDependent Choices and Weak Compactness
We work in set-theory without the Axiom of Choice ZF. We prove that the principle of Dependent Choices (DC) implies that the closed unit ball of a uniformly convex Banach space is weakly compact, and in particular, that the closed unit ball of a Hilbert space is weakly compact. These statements are not provable in ZF, and the latter statement does not imply DC. Furthermore, DC does not imply th...
متن کاملA Weak Grothendieck Compactness Principle
The Grothendieck compactness principle states that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. In this article, an analogue of the Grothendieck compactness principle is considered when the norm topology of a Banach space is replaced by its weak topology. It is shown that every weakly compact subset of a Banach space is contained in...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 1973
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm-49-1-35-40