compact bilinear operators
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2020 ◽  
Vol 10 (02) ◽  
pp. 2050002
Author(s):  
Mieczysław Mastyło ◽  
Eduardo B. Silva

This paper is devoted to the study of the stability of the compactness property of bilinear operators acting on the products of interpolated Banach spaces. We prove one-sided compactness results for bilinear operators on products of Banach spaces generated by abstract methods of interpolation, in the sense of Aronszajn and Gagliardo. To get these results, we prove a key one-sided bilinear interpolation theorem on compactness for bilinear operators on couples satisfying an extra approximation property. We give applications to general cases, including Peetre’s method and the general real interpolation methods.


2018 ◽  
Vol 291 (14-15) ◽  
pp. 2168-2187 ◽  
Author(s):  
Fernando Cobos ◽  
Luz M. Fernández-Cabrera ◽  
Antón Martínez

2017 ◽  
Vol 24 (5) ◽  
pp. 1181-1203 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez

2017 ◽  
Vol 290 (11-12) ◽  
pp. 1663-1677 ◽  
Author(s):  
Luz M. Fernández-Cabrera ◽  
Antón Martínez

2013 ◽  
Vol 141 (10) ◽  
pp. 3609-3621 ◽  
Author(s):  
Árpád Bényi ◽  
Rodolfo H. Torres

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