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Multi-valued Operators/Linear Relations Between Kreĭn Spaces

In: Operator Theory

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  • HendrikLuit Wietsma

    (Department of Mathematics, Stockholm University)

Abstract

Here an introduction to linear spaces with an indefinite inner product, the so-called Kreĭn spaces, and to multi-valued operators between them is given. More precisely, the basic properties of these indefinite inner product spaces, which are generalizations of Hilbert spaces, are described, where the similarities to and differences compared with Hilbert spaces are emphasized. Secondly, the basic properties of multi-valued operators, which are generalizations of (linear) operators, are presented; such operators appear naturally, for instance, in the treatment of differential equations.

Suggested Citation

  • HendrikLuit Wietsma, 2015. "Multi-valued Operators/Linear Relations Between Kreĭn Spaces," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 8, pages 151-163, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_39
    DOI: 10.1007/978-3-0348-0667-1_39
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