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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

Δεληγιάννη, Ειρήνη Α

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.

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

School/Department--School of Sciences and Engineering--Department of Mathematics--Doctoral theses

Type of Work--Doctoral theses

Views

848

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