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On quasiaffinity and quasiaffine inverses of partial isometries. (English) Zbl 1064.47501

Summary: It is a well-known fact in operator theory that an invertible partial isometry is unitary. In this note, we show that a relaxation of invertibility to the concept of quasiaffine inverse or mere quasiaffinity of a partial isometry will still give us the result that it is unitary. We also deduce results concerning quasi-similarity of partial isometrics.

MSC:

47A65 Structure theory of linear operators
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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