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Identifier |
uch.math.phd//1995DIS0132 |
Title |
Αναδρομικά οριζόμενες νόρμες και εφαρμογές τους σε προβλήματα παραμόρφωσης και ύπαρξης unconditional βάσης σε χώρους Banach |
Alternative Title |
Recursively defined norms and their applications on problems of distortion and existence of unconditional bases in banach spaces |
Author
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Δεληγιάννη, Ειρήνη Α
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Abstract |
Given a family of finite subjects of N, sequence E1 < E2 < .... < Ed of successive intervals of N is called M - admissible if there exists a set {m1,...,md} E M such that m1 <= E1 < m2 <= E2 < ... < md <= Ed. A Banach space X with a normalized basis (en)oo n=1 is said to have a saturated norm if there exist a sequence (Mk)k of compact families of finite subsets of N and a sequence (Θκ)κ of positive reals, with 0 < Θk < 1 and Θκ ---> 0, such that the norm ΙΙ.ΙΙ of X satisfies the following implicit equation: (τύπος) is a Mk - admissible sequence of intervals For given sequences (Mk)k and (Θk)k the above equation determines a unique Banach space which we denote by T[(Mk,Θκ)κ]. The prototype of such spaces is Tsirelson's space. Next we consider particular cases of spaces of the form T[(Mk, Θκ)oo k=1] which we show to admit naturally defined arbitrarily large distortions. In particular, we give an example of an arbitrarily distortable asymptotic l1 Banach space with an unconditional basis, answering a question in [G3]. Finally, using the previous construction and ideas from [G-M], we produce an asymptotic l1 Banach space not containing any unconditional basic sequence.
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Language |
Greek |
Subject |
ΧΩΡΟΣ BANACH; ΒΑΣΗ ΕΝΟΣ ΧΩΡΟΥ BANACH; ΠΑΡΑΜΟΡΦΩΣΗ; ΚΟΡΕΣΜΕΝΗ ΝΟΡΜΑ; UNCONDITIONAL ΒΑΣΗ; ΑΣΥΜΠΤΩΤΙΚΑ - LP ΧΩΡΟΣ BANACH; BANACH SPACE; BASIS OF A BANACH SPACE; DISTORTION; SATURATED NORM; UNCONDITIONAL BASIS; ASYMPTOTIC - LP BANACH SPACE |
Issue date |
1995-07-19 |
Collection
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School/Department--School of Sciences and Engineering--Department of Mathematics--Doctoral theses
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Type of Work--Doctoral theses
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Permanent Link |
https://elocus.lib.uoc.gr//dlib/a/4/9/metadata-dlib-1995DIS0132.tkl
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Views |
853 |