Complementarity of subspaces of ℓ revisited

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Abstract

We present a simple criterion for complementarity of subspaces of ℓ induced by certain bounded linear operators. As applications, it is shown that some typical and well-known subspaces such as mean or almost convergent sequence spaces are uncomplemented in ℓ . We also note that there exists a weak closed uncomplemented subspace of ℓ .

Original languageEnglish
Article numberOaM-12-66
Pages (from-to)1089-1097
Number of pages9
JournalOperators and Matrices
Volume12
Issue number4
DOIs
Publication statusPublished - 1 Dec 2018

Keywords

  • Almost convergence
  • Bounded sequence
  • Complemented subspace
  • Matrix representation
  • Mean convergence

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