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An algebraic characterization of complete inner product spaces

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  • Vasile I. Istratescu

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.

Suggested Citation

  • Vasile I. Istratescu, 1986. "An algebraic characterization of complete inner product spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:192604
    DOI: 10.1155/S0161171286000066
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