Embeddings between Lorenz sequence spaces are strictly singular

Jan Lang; Ales Nekvinda

Embeddings between Lorenz sequence spaces are strictly singular

Functional Analysis 2022-03-15 v2

Authors: Jan Lang , Ales Nekvinda

Abstract

Given $0<p,q, r<\infty$ and $q<r\le \infty$ we consider the natural embedding $\ell_{p,q}\hookrightarrow \ell_{p,r}$ between Lorenz sequence spaces. We prove that this non-compact embedding is always strictly singular but not finitely strictly singular.

Keywords

metric embeddings

Cite

@article{arxiv.2104.00471,
  title  = {Embeddings between Lorenz sequence spaces are strictly singular},
  author = {Jan Lang and Ales Nekvinda},
  journal= {arXiv preprint arXiv:2104.00471},
  year   = {2022}
}

Comments

19 pages

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