Open AccessApproximation numbers of matrix transformations and inclusion maps
Author(s) -
Manika 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 $1leq pleq infty$.