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<p>We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a suitable pair of closed subspaces. We investigate into these classes of pairs of subspaces and describe several applications to define some notions of indecomposability for Banach spaces and to extend definitions from the case of bounded operators to the case of closed operators.</p>

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Tauberian pairs of closed subspaces of a Banach space

  • 期刊论文

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  • 发表日期：

    2026年4月13日

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  • Manuel González,
  • Antonio Martínez-Abejón

摘要

We introduce the notions of tauberian, cotauberian and weakly compact pair of closed subspaces of a Banach space. The theory produced by these notions is richer than that of the corresponding operators since an operator can be regarded as a suitable pair of closed subspaces. We investigate into these classes of pairs of subspaces and describe several applications to define some notions of indecomposability for Banach spaces and to extend definitions from the case of bounded operators to the case of closed operators.