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Banach space theory
"... The workshop was largely motivated by the recent extraordinary work of Argyros and Haydon [AH] (discussed below) which, following on the fundamental work of Gowers and Maurey in the 1990's, continued the discovery of the incredible variety of possible Banach space structure. [AH] is connected ..."
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The workshop was largely motivated by the recent extraordinary work of Argyros and Haydon [AH] (discussed below) which, following on the fundamental work of Gowers and Maurey in the 1990's, continued the discovery of the incredible variety of possible Banach space structure. [AH
Compactness in Banach space theory  selected problems
 REV R. ACAD CIEN SERIE A. MAT
"... We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and RadonNikodým compacta. ..."
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Cited by 2 (0 self)
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We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and RadonNikodým compacta.
Separable Banach space theory needs strong set existence axioms
 TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
, 1996
"... We investigate the strength of set existence axioms needed for separable Banach space theory. We show that a very strong axiom, Π1 1 comprehension, is needed to prove such basic facts as the existence of the weak∗ closure of any normclosed subspace of ℓ1 = c ∗ 0. This is in contrast to earlier w ..."
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Cited by 7 (5 self)
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We investigate the strength of set existence axioms needed for separable Banach space theory. We show that a very strong axiom, Π1 1 comprehension, is needed to prove such basic facts as the existence of the weak∗ closure of any normclosed subspace of ℓ1 = c ∗ 0. This is in contrast to earlier
On certain classes of Baire1 functions with applications to Banach space theory
 Functional Analysis Proceedings, The University of Texas at Austin 1987–89, Lecture Notes in Math
, 1991
"... Certain subclasses of B1(K), the Baire1 functions on a compact metric space K, are defined and characterized. Some applications to Banach spaces are given. 0. Introduction. Let X be a separable infinite dimensional Banach space and let K denote its dual ball, Ba(X ∗), with the weak * topology. K is ..."
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Cited by 19 (12 self)
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Certain subclasses of B1(K), the Baire1 functions on a compact metric space K, are defined and characterized. Some applications to Banach spaces are given. 0. Introduction. Let X be a separable infinite dimensional Banach space and let K denote its dual ball, Ba(X ∗), with the weak * topology. K
Infinite Combinatorics and Applications to Banach space Theory Course Notes: Math 663601
, 2015
"... 2In this course we discuss several results on Infinite Combinatorics, and their applications to Banach space theory. In the first chapter we present Ramsey’s theorem for infinite subsets of the natural numbers. Assume you color all infinite subsequences of the natural numbers N using finitely many ..."
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2In this course we discuss several results on Infinite Combinatorics, and their applications to Banach space theory. In the first chapter we present Ramsey’s theorem for infinite subsets of the natural numbers. Assume you color all infinite subsequences of the natural numbers N using finitely many
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