ACTA issues

The Bishop--Phelps--Bollobás modulus for operators

Francisco Javier García-Pacheco, Soledad Moreno-Pulido

Acta Sci. Math. (Szeged) 85:1-2(2019), 189-201

Abstract. A modulus for the Bishop--Phelps--Bollobás property for operators (BPBpo) is formerly introduced in the literature that characterizes whether a pair of Banach spaces enjoys the BPBpo and that also provides the best possible value of the BPBpo for a given pair of Banach spaces that enjoys it. We use it also to show that the BPBpo is hereditary to a class of complemented subspaces that strictly includes the $M$-summands. We also provide an equivalent reformulation of this modulus. Finally, the continuity properties of this modulus are also discussed.

DOI: 10.14232/actasm-018-765-5

AMS Subject Classification (1991): 47A05, 46B20

Keyword(s): Bishop--Phelps--Bollobás modulus, continuous linear operator, complemented subspace

Received January 19, 2018 and in final form April 24, 2018. (Registered under 15/2018.)