Multi-valued Operators/Linear Relations Between Kreĭn Spaces

HendrikLuit Wietsma ()
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HendrikLuit Wietsma: Department of Mathematics, Stockholm University

Chapter 8 in Operator Theory, 2015, pp 151-163 from Springer

Abstract: 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.

Keywords: Hilbert Space; Closed Subspace; Orthogonal Complement; Canonical Decomposition; Pontryagin Space (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0667-1_39

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DOI: 10.1007/978-3-0348-0667-1_39

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