The work on which this paper is based was done while the author was an Atomic Energy Commission Pre-doctoral Fellow at the University of Chicago. The paper is essentially part of the dissertation submitted in candidacy for the Ph.D. degree. The author wishes to express his gratitude to Professor Paul Halmos for his helpful suggestions and criticism during the preparation of the paper. * Numbers in brackets refer to the list of references at the end of the paper. 3 This § (including Lemma 2.1) is only a recapitulation of the known theory of linear isometries. A thoroughgoing exposition including proofs may be found in [3].
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