A forgotten theorem of Orty\'nski, not far off

Félix Cabello Sánchez; Jesús M. F. Castillo; Yolanda Moreno Salguero

A forgotten theorem of Orty\'nski, not far off

Functional Analysis 2024-06-18 v2

Authors: Félix Cabello Sánchez , Jesús M. F. Castillo , Yolanda Moreno Salguero

Abstract

We combine techniques of Orty\'nski \cite{orty} and Moreno and Plichko \cite{moreplic} to show that, for $0<p<\infty$ , every subspace of $\ell_p(\Gamma)$ having density character $\mathfrak m$ has the form $\ell_p(\mathfrak m, H_m)$ for some family of subspaces $H_m\subset \ell_p$ . The ideas of Orty\'nski are then applied to obtain unique positions for Lindenstrauss spaces.

Keywords

l_p spaces subspaces density character lindenstrauss spaces interpolation banach space theory

Cite

@article{arxiv.2204.00670,
  title  = {A forgotten theorem of Orty\'nski, not far off},
  author = {Félix Cabello Sánchez and Jesús M. F. Castillo and Yolanda Moreno Salguero},
  journal= {arXiv preprint arXiv:2204.00670},
  year   = {2024}
}

Comments

The paper must be withdrawn because it contains a wrong proof

A forgotten theorem of Orty\'nski, not far off

Abstract

Keywords

Cite

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