6th Summer Workshop on Operator Theory

9th - 13th July 2018 Kraków

Alan Kamuda

Towards Theory of Frames in Krein Spaces

During the first part of the talk we discuss the difference between two contemporary definitions of frames in Krein spaces. The first definition, was introduced in 2012 by Julian I. Giribet et al. [1] and called J-frame. The second one was defined in 2015 by Kevin Esmeral et al. [2]. We briefly mention conclusions related to these definitions and properties of associated frame operators. In the second part, according to [3], we introduce a new definition of frames in Krein spaces which generalizes the previous ones and fits well the ideology of Krein spaces. In the last part we present the methodology of J-frame construction with using the conventional frame from Hilbert space and we present two examples of J-frames.

The talk is based on the following papers.

  1. J. I. Giribet, A. Maestripieri, F. Martinez Peria, P. G. Massey : On frames for Krein spaces, J. Math. Anal. Appl., 393 (2012).
  2. K. Esmeral, O. Ferrer, E. Wagner:  Frames in Krein spaces arising from a non-regular W-metric, Banach J. Math. Anal. 9:1, (2015) 1-16.
  3. S. Kużel, A. Kamuda: On J-frames related to maximal definite subspaces, Annals of Functional Analysis, accepted for publication.
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