On (a, B, c)-ideals in Banach spaces | Zendy

Ksenia Niglas | Zendy; Indrek Zolk | Zendy

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On (a, B, c)-ideals in Banach spaces

Author(s) -

Ksenia Niglas,

Indrek Zolk

Publication year - 2014

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2014.18.11

Subject(s) - ideal (ethics) , mathematics , linear subspace , banach space , subspace topology , pure mathematics , transitive relation , type (biology) , discrete mathematics , combinatorics , mathematical analysis , ecology , philosophy , epistemology , biology

In this paper we focus on subspaces of Banach spaces that are ( a , B , c )-ideals. We study ( a , B , c )-ideals in l 2 ∞ and present easily verifiable conditions for a subspace of l 2 ∞ to be an ( a , B , c )-ideal. Our main results concern the transitivity of ( a , B , c )-ideals. We show that if X is an ( a , B , c )-ideal in Y and Y is a ( d , E , f )-ideal in Z , then X is a certain type of ideal in Z . Relying on this result, we show that if X is an ( a , B , c )-ideal in its bidual, then X is a certain type of ideal in X (2 n ) for every n ∈ N.

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