International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 1, Pages 47-53
doi:10.1155/S0161171286000066
An algebraic characterization of complete inner product spaces
Universitat Konstz, Fakultat fur Mathematik, Posfach 55 60, Konstanz 1 D-7750, Germany
Received 1 October 1983
Copyright © 1986 Vasile I. Istratescu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We present a characterization of complete inner product spaces using en involution on the set of all bounded linear operators on a Banach space. As a metric conditions we impose a “multiplicative” property of the norm for hermitain operators. In the second part we present a simpler proof (we believe) of the Kakutani and Mackney theorem on the characterizations of
complete inner product spaces. Our proof was suggested by an ingenious proof of a similar result obtained by N. Prijatelj.