RT journal article
T1 Bishop-Phelps-Bollobás Moduli of a Banach space
A1 Chica, Mario
A1 Kadets, Vladimir
A1 Martín, Miguel
A1 Moreno Pulido, Soledad
A1 Rambla Barreno, Fernando
A2 Matemáticas
K1 Banach space
K1 Bounded linear operator
K1 Approximation
K1 Uniformly non-square spaces
AB We introduce two Bishop–Phelps–Bollobás moduli of a Banach space which measure, for a given Banach space, what is the best possible Bishop–Phelps–Bollobás theorem in this space. We show that there is a common upper bound for these moduli for all Banach spaces and we present an example showing that this bound is sharp. We prove the continuity of these moduli and an inequality with respect to duality. We calculate the two moduli for Hilbert spaces and also present many examples for which the moduli have the maximum possible value (among them, there are C(K) spaces and L1(μ) spaces). Finally,we show that if a Banach space has the maximum possible value of any of the moduli, then it contains almost isometric copies of the real space l^2_∞ and present an example showing that this condition is not sufficient.
PB Elsevier
SN 0022-247X
YR 2014
FD 2014
LK http://hdl.handle.net/10498/30490
UL http://hdl.handle.net/10498/30490
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 12-nov-2026