Approximation numbers of matrix transformations and inclusion maps | Zendy

Maneesha Gupta | Zendy; Lipi Acharya | Zendy

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Approximation numbers of matrix transformations and inclusion maps

Author(s) -

Maneesha Gupta,

Lipi Acharya

Publication year - 2011

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.42.2011.924

Subject(s) - mathematics , lambda , banach space , sequence (biology) , diagonal , scalar (mathematics) , characterization (materials science) , space (punctuation) , combinatorics , sequence space , matrix (chemical analysis) , operator (biology) , discrete mathematics , geometry , physics , linguistics , philosophy , materials science , biochemistry , repressor , chemistry , biology , gene , transcription factor , optics , composite material , genetics

In this paper we establish relationships of the approximation numbers of matrix transformations acting between the vector-valued sequence spaces spaces of the type $lambda(X)$ defined corresponding to a scalar-valued sequence space $lambda$ and a Banach space $(X,|.|)$ as $$lambda(X)={overline x={x_i}: x_iin X, forall~iin mathbb{N},~{|x_i|_X}in lambda};$$ with those of their component operators. This study leads to a characterization of a diagonal operator to be approximable. Further, we compute the approximation numbers of inclusion maps acting between $ell^p(X)$ spaces for $1leq pleq infty$.

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