Multi-valued Operators/Linear Relations Between Kreı̆n Spaces

Hendrik Luit Wietsma ()
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Hendrik Luit Wietsma: Stockholm University, Department of Mathematics

Chapter 10 in Operator Theory, 2026, pp 261-274 from Springer

Abstract: Abstract Here an introduction to linear spaces with an indefinite inner product, the so-called Kreı̆n 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.

Date: 2026
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DOI: 10.1007/978-3-032-16356-1_39

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