Interpolation of bilinear operators and compactness

Eduardo Brandani da Silva; Dicesar Lass Fernandez

Interpolation of bilinear operators and compactness

Functional Analysis 2012-06-04 v1

Authors: Eduardo Brandani da Silva , Dicesar Lass Fernandez

Abstract

The behavior of bilinear operators acting on interpolation of Banach spaces for the $\rho$ method in relation to the compactness is analyzed. Similar results of Lions-Peetre, Hayakawa and Person's compactness theorems are obtained for the bilinear case and the $\rho$ method.

Keywords

operator theory on banach spaces banach space interpolation theory

Cite

@article{arxiv.1206.0017,
  title  = {Interpolation of bilinear operators and compactness},
  author = {Eduardo Brandani da Silva and Dicesar Lass Fernandez},
  journal= {arXiv preprint arXiv:1206.0017},
  year   = {2012}
}

Comments

This work was published at "Nonlinear Analysis: Theory, Methods and Applications, Volume 73, Issue 2, 2010, Pages 526-537". Since there are some gaps in the original proof of Theorem 4.3, Here we give a new proof. For this, we change the Lemma 4.2

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