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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Interpolation of the measure of noncompactness of bilinear operators


Authors: Mieczysław Mastyło and Eduardo B. Silva
Journal: Trans. Amer. Math. Soc. 370 (2018), 8979-8997
MSC (2010): Primary 46B70, 47B07; Secondary 47B38, 42B20
DOI: https://doi.org/10.1090/tran/7501
Published electronically: September 18, 2018
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Abstract: We study interpolation of the measure of noncompactness of bilinear operators. We prove a result of a general nature which states that for a large class of interpolation functors preserving bilinear interpolation estimates of measures of noncompactness of interpolated linear operators between Banach couples can be lifted to bilinear operators. As an application, we show that the measure of noncompactness of bilinear operators behave well under the real method of interpolation.


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Additional Information

Mieczysław Mastyło
Affiliation: Faculty of Mathematics and Computer Sciences, Adam Mickiewicz University in Poznań, 61-614 Poznań, Poland
Email: mastylo@amu.edu.pl

Eduardo B. Silva
Affiliation: Departamento de Matemática, Universidade Estadual de Maringá, Maringá, Paraná, 870300-110, Brazil
Email: ebsilva@uem.br

DOI: https://doi.org/10.1090/tran/7501
Keywords: Measure of noncompactness, bilinear compact operators, interpolation functor, interpolation spaces
Received by editor(s): July 15, 2017
Received by editor(s) in revised form: September 29, 2017, and November 17, 2017
Published electronically: September 18, 2018
Additional Notes: The first-named author was supported by the National Science Centre, Poland, project no. 2015/17/B/ST1/00064.
Article copyright: © Copyright 2018 American Mathematical Society

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