z-logo
Premium
A Sequentially Unconditional Banach Space with Few Operators
Author(s) -
Argyros S. A.,
Manoussakis A.
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015388
Subject(s) - mathematics , banach space , schauder basis , subsequence , infinite dimensional vector function , injective function , function space , pure mathematics , sequence (biology) , discrete mathematics , eberlein–šmulian theorem , reflexive space , lp space , interpolation space , mathematical analysis , functional analysis , gene , biology , bounded function , genetics , biochemistry , chemistry
A Banach space X is said to be sequentially unconditional if every Schauder basic sequence has an unconditional subsequence. We provide an example of a reflexive Banach space X isu which is sequentially unconditional and such that every T ∈ L( X isu ) is a strictly singular perturbation of a multiple of the identity. The space X isu belongs to the class of Banach spaces with saturated and conditional structure. Constructing X isu we follow the general scheme invented by W. T. Gowers and B. Maurey in their celebrated construction of a Hereditarily Indecomposable Banach space. The new ingredient concerns the definition of the special (conditional) functionals. For this we use a non‐injective coding function σ in conjunction with a Baire‐like property of a sequence of countable trees stated and proved in the present paper. It is worth mentioning that X isu admits a richer unconditional structure than classical spaces like L 1 (0,1) and it remains unsettled whether X isu is a subspace of a Banach space with an unconditional basis. 2000 Mathematics Subject Classification 46B20, 46B45 (primary), 05D99, 47L05 (secondary).

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here