Full paper in PDF:
$%A. Rodríguez Palacios, Multiplicative characterization of Hilbert spaces and other interesting classes of Banach spaces, Rev. Mat. Univ. Complut. Madrid 9 (1996), supplementary, 149189.%$

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 X  , we show how the existence of a norm-one element u  in X  and a norm-one continuous bilinear mapping f :X × X --> X  satisfying f(x,u)= f(u,x)= x  for all x  in X  , together with some more intrinsic conditions, can be utilized to characterize X  as a member of some relevant subclass of the class of Banach spaces.

1991 Mathematics Subject Classification: 46C15, 46K70, 46B08, 17C65.