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

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.