Uniform openness of multiplication in Banach spaces $L_p$

Marek Balcerzak; Adam Majchrzycki; Filip Strobin

Uniform openness of multiplication in Banach spaces $L_p$

Functional Analysis 2013-09-16 v1

Authors: Marek Balcerzak , Adam Majchrzycki , Filip Strobin

Abstract

We show that multiplication from $L_p\times L_q$ to $L_1$ (for $p,q\in [1,\infty]$ , $1/p+1/q=1$ ) is a uniformly open mapping. We also prove the uniform openness of the multiplication from $\ell_1\times c_0$ to $\ell_1$ . This strengthens the former results obtained by M. Balcerzak, A. Majchrzycki and A. Wachowicz.

Keywords

uniform openness multiplication mapping banach spaces $l_p$ spaces $l_1$ space $c_0$ space

Cite

@article{arxiv.1309.3433,
  title  = {Uniform openness of multiplication in Banach spaces $L_p$},
  author = {Marek Balcerzak and Adam Majchrzycki and Filip Strobin},
  journal= {arXiv preprint arXiv:1309.3433},
  year   = {2013}
}

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8 pages

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