Compressions of maximal dissipative and self-adjoint linear relations and of dilations☆,☆☆

Dedicated to Harm Bart – a fine colleague and good friend.
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Abstract

In this paper we generalize results from Stenger (1968) [30], Nudelman (2011) [28] and Azizov and Dijksma (2012) [7] to maximal dissipative and self-adjoint linear relations and discuss related results for nonnegative self-adjoint extensions of nonnegative symmetric linear relations and self-adjoint dilations of maximal dissipative linear relations.

AMS classification

47A06
47A20
47B44
47B25
47B50

Keywords

Hilbert space
Krein space
Symmetric
Self-adjoint
Dissipative
Maximal dissipative
Linear relation
Dilation
Compression
Reproducing kernel
Codimension

Cited by (0)

☆

The research of T.Ya. Azizov was supported by grant 12-01-00102-a of the RFBR. A. Dijksma thanks the Department of Mathematics and Statistics of the Sultan Qaboos University, Muscat, Oman, and G. Wanjala for their hospitality.

☆☆

In [7] this paper was announced under the tentative title: Reproducing kernels and compression of linear relations.

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