Embedding  l  ∞  into the Space of Bounded Operators on Certain Banach Spaces | Zendy

Androulakis G. | Zendy; Beanland K. | Zendy; Dilworth S. J. | Zendy; Sanacory F. | Zendy

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Embedding l ∞ into the Space of Bounded Operators on Certain Banach Spaces

Author(s) -

Androulakis G.,

Beanland K.,

Dilworth S. J.,

Sanacory F.

Publication year - 2006

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609306018868

Subject(s) - mathematics , banach space , bounded function , embedding , space (punctuation) , sequence (biology) , basis (linear algebra) , mathematics subject classification , discrete mathematics , linear operators , pure mathematics , sequence space , approximation property , combinatorics , mathematical analysis , geometry , linguistics , philosophy , artificial intelligence , biology , computer science , genetics

Sufficient conditions are given on a Banach space X which ensure that embeds in L( X ), the space of all bounded linear operators on X . A basic sequence e n is said to be quasisubsymmetric if for any two increasing sequences ( k n ) and ( l n ) of positive integers with ( k n ) ⩽ ( l n ) for all n , ( e k n) dominates ( e l n). If a Banach space X has a seminormalized quasisubsymmetric basis then l ∞ embeds in l ( X ). 2000 Mathematics Subject Classification 46B28 (primary), 46B03 (secondary).

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