Full paper in PDF:
$%A. Rodríguez Palacios, Multiplicative characterization of Hilbert spaces and other interesting
classes of Banach spaces, Rev. Mat. Univ. Complut. Madrid 9 (1996), supplementary, 149–189.%$
Multiplicative Characterization of Hilbert
Spaces and Other Interesting Classes of
Banach Spaces
Ángel RODRíGUEZ
PALACIOS
Departamento de Análisis Matemático
Facultad de Ciencias
Universidad de Granada
18071 Granada — Spain
Received: May 23, 1996
ABSTRACT
For a Banach space
, we show how the existence of a norm-one element
in
and a norm-one continuous bilinear mapping
satisfying
for all
in
, together with some more intrinsic
conditions, can be utilized to characterize
as a member of some relevant
subclass of the class of Banach spaces.
1991 Mathematics Subject Classification: 46C15, 46K70, 46B08, 17C65.