Abstract
The results of V.P. Potapov, relating to geometric questions of matrix theory in spaces with an indefinite metric, are concentrated mainly in his fundamental research [16]. His ideas were the basis of investigations of a series of authors; in some cases without these authors being aware of the fact that their research was rooted in Potapov–s work (as, for example, Colpa [3] and Ikramov [6]). Our survey does not claim to be a complete reflection of V.P. Potapov–s ideas in the field mentioned and it is concentrated around three objects closest to us: the criterion of doubleness of J-nonexpansive operators, J-polar representation of plus-operators and factorization of J-nonnegative operators.
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