2019/04/13 by Mastyło, Mieczysław, Silva, Eduardo B.
#46B70 #47B07 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1904.06523
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 abstract methods of interpolation in the senseof Aronszajn and Gagliardo. A key step is to show an one-sided bilinear interpolation theorem on compactness for bilinear operators on couples satisfying an approximation property. We show applications to general cases, including Peetre's method and the general real interpolation methods.