On interpolation of Asplund operators

Abstract

We study the interpolation properties of Asplund operators by the complex method, as well as by general J -and K-methods. (2000): 46B70, 47B10 Mathematics Subject Classification

A Bishop-Phelps-Bollobás theorem for bounded analytic functions

“…[12]). For more information and recent development on Asplund spaces, we refer the reader to [10,14].…”

On interpolation of weakly compact bilinear operators

“…Next we establish an auxiliary result involving linear operators and the upper complex method. For the proof we follow an idea of [7,Corollary 3.4].…”

“…Next we establish an auxiliary result involving linear operators and the upper complex method. For the proof we follow an idea of [7, Corollary 3.4]. Lemma Let $$\bar{A}=\big (A_0,A_1\big )$$, $$\bar{B}=\big (B_0,B_1\big )$$ be Banach couples and let $$R: A_0+ A_1 \longrightarrow B_0+B_1$$ be a linear operator such that the restrictions $$R: A_j \longrightarrow B_j$$ are bounded for $$j=0,1$$, and one of the two restrictions is weakly compact.…”