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Banded perturbations of the unit vector basis in some sequence spaces

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Abstract

Perturbations of the unit vector basis of the formX n =Σ¦j−n¦≦m a nj e j wherem is a fixed positive integer are investigated. It is shown that if |a nj |≦1 and if {x n } possesses a biorthogonal sequence uniformly bounded inl p for some 1<=p<∞, then {x n } is a seminormalized basic sequence in some reflexive Orlicz spacel N, then {xn} is equivalent to {e n} inl N.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, Georgia, USA

    Alfred D. Andrew & Stephen Demko

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  1. Alfred D. Andrew
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  2. Stephen Demko
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Andrew, A.D., Demko, S. Banded perturbations of the unit vector basis in some sequence spaces. Israel J. Math. 29, 389–392 (1978). https://doi.org/10.1007/BF02761176

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  • DOI: https://doi.org/10.1007/BF02761176

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