ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47 A05, 47 B15, 47 B50 Gebel, Michael, Institute of Applied Mathematics I, Technical University Bergakademie Freiberg, Germany Spectral Theory of Adjointable Operators in Spaces with two Metrics If a Banach space is embedded in a Hilbert or Kreĭn space, one says that we are given a space with two metrics. We consider linear operators acting in such spaces, for which there exists a suitably defined adjoint operator with respect to the second metric. The theory of these adjointable operators originates in a pioneering paper of Kreĭn [1947], and has been reconsidered by a number of authors since then. We present a unifying treatment of these development as well as some new results. The theory of symmetrizable and normalizable operators is covered as a special case. Applications to the theory of definitizable operators in Kreĭn spaces are indicated. The results have been partly obtained in joint work with Th. Ya. Azizov, Voronesh University, Russia.