An algebraic characterization of complete inner product spaces

Vasile I. Istratescu

International Journal of Mathematics and Mathematical Sciences, 1986, vol. 9, 1-7

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.

Date: 1986
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:192604

DOI: 10.1155/S0161171286000066

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