# Interpolation of bilinear operators and compactness

@article{Silva2010InterpolationOB, title={Interpolation of bilinear operators and compactness}, author={Eduardo Brandani da Silva and Dicesar Lass Fernandez}, journal={arXiv: Functional Analysis}, year={2010} }

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.

## 14 Citations

Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces

- Mathematics, Computer ScienceJ. Approx. Theory
- 2019

Working in the setting of quasi-Banach couples, a formula is established for the measure of non-compactness of bilinear operators interpolated by the general real method.

Interpolation of compact bilinear operators

- Mathematics
- 2019

We investigate the stability of compactness of bilinear operators acting on the product of interpolation of Banach spaces. We develop a general framework for such results and our method applies to…

Interpolation of compact bilinear operators among quasi-Banach spaces and applications

- Mathematics
- 2018

We study the interpolation properties of compact bilinear operators by the general real method among quasi‐Banach couples. As an application we show that commutators of Calderon–Zygmund bilinear…

On interpolation properties of compact bilinear operators

- Mathematics
- 2017

We investigate interpolation properties of compact bilinear operators under the general real method. Results apply in particular to the real method with a function parameter and also to the complex…

On the interpolation of the measure of non-compactness of bilinear operators with weak assumptions on the boundedness of the operator

- Mathematics
- 2021

Abstract We complete the range of the parameters in the interpolation formula established by Mastylo and Silva for the measure of non-compactness of a bilinear operator interpolated by the real…

A compactness result of Janson type for bilinear operators

- Mathematics
- 2021

We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.

The Australian Journal of Mathematical Analysis and Applications

- 2017

Positive and regular bilinear operators on quasi-normed functional spaces are introduced and theorems characterizing compactness of these operators are proved. Relations between bilinear operators…

Interpolation of Holomorphic functions

- Mathematics
- 2017

Interpolation Theory gives techniques for constructing spaces from two initial Banach spaces. We provide several conditions under which the restriction of a holomorphic map f : X0 +X1 → Y0 +Y1 to the…

Real Interpolation of Compact Bilinear Operators

- Mathematics
- 2018

We establish an analog for bilinear operators of the compactness interpolation result for bounded linear operators proved by Cwikel and Cobos, Kühn and Schonbek. We work with the assumption that…

Compact Bilinear Operators and Commutators

- Mathematics
- 2013

First published in Proceedings of the American Mathematical Society, volume 141, published by the American Mathematical Society. Also available electronically from…

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