RMC - Vol. 9, supplementary - A. Rodríguez Palacios

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 $X$ , 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.