This is an announcement for the paper "The Bishop-Phelps-Bollob'{a}s theorem for operators on $L_1(\mu)$" by Yun Sung Choi, Sun Kwang Kim, Han Ju Lee and Miguel Martin.

Abstract: In this paper we show that the Bishop-Phelps-Bollob'as theorem holds for $\mathcal{L}(L_1(\mu), L_1(\nu))$ for all measures $\mu$ and $\nu$ and also holds for $\mathcal{L}(L_1(\mu),L_\infty(\nu))$ for every arbitrary measure $\mu$ and every localizable measure $\nu$. Finally, we show that the Bishop-Phelps-Bollob'as theorem holds for two classes of bounded linear operators from a real $L_1(\mu)$ into a real $C(K)$ if $\mu$ is a finite measure and $K$ is a compact Hausdorff space. In particular, one of the classes includes all Bochner representable operators and all weakly compact operators.

Archive classification: math.FA

Mathematics Subject Classification: Primary 46B20, Secondary 46B04, 46B22

Submitted from: hanjulee@dongguk.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1303.6078

or

http://arXiv.org/abs/1303.6078