The Development of Some of V.P. Potapov’s Ideas the Geometric Theory of Operators in Spaces with Indefinite Metric

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.