Generalized resolvents of isometric linear relations in Pontryagin spaces. I: Foundations. (English) Zbl 0953.46012
Adamyan, V. M. (ed.) et al., Operator theory and related topics. Proceedings of the Mark Krein international conference on operator theory and applications, Odessa, Ukraine, August 18-22, 1997. Volume II. Basel: Birkhäuser. Oper. Theory, Adv. Appl. 118, 303-319 (2000).
The author develops a theory of (multi-valued) linear relations on a Krein space and, in particular, of isometric and unitary relations on a Pontryagin space. Various elementary properties of such linear relations are derived. The theory is then applied to linear stationary conservative discrete-time systems with Pontryagin state spaces.
For the entire collection see [Zbl 0934.00033].
For the entire collection see [Zbl 0934.00033].
Reviewer: Cornelis van der Mee (Cagliari)
MSC:
| 46B50 | Compactness in Banach (or normed) spaces |
| 47A06 | Linear relations (multivalued linear operators) |
| 46C20 | Spaces with indefinite inner product (Kreĭn spaces, Pontryagin spaces, etc.) |
| 47A10 | Spectrum, resolvent |
