[Banach] Abstract of a paper by Maria D. Acosta

This is an announcement for the paper "The Bishop-Phelps-Bollob'{a}s property for operators on $C(K)$" by Maria D. Acosta.

Abstract: We provide a version for operators of the Bishop-Phelps-Bollob'{a}s Theorem when the domain space is the complex space $C_0(L)$. In fact we prove that the space of weakly compact operators from the complex space $C_0(L)$ into a ${\mathbb C}$-uniformly convex space satisfies the Bishop-Phelps-Bollob'{a}s property for operators. As a consequence, in the complex case, the space of operators from $C_0(L)$ into $L_p (\mu)$ ($1 \le p < \infty $) satisfies the Bishop-Phelps-Bollob'{a}s property for operators.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B28, 47B99

Submitted from: dacosta@ugr.es

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

http://front.math.ucdavis.edu/1405.6428

or

http://arXiv.org/abs/1405.6428