Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-27T19:37:39.510Z Has data issue: false hasContentIssue false
  • English
  • Français

Subnormality and generalized commutation relations

Published online by Cambridge University Press:  18 May 2009

Jerzy Bartłomiej Stochel
Jerzy Bartłomiej Stochel
Affiliation:
Fachbereich Mathematik, der Johann Wolfang Goethe Universität, Robert-Mayer-Strage 6–10, Postfach 11 19 32, 6000 frankfurt am Main 11, Federal Republik of Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In the theory of Hilbert space operators an important question is whether an operator is subnormal [3], [4], [7], [8]. A densely defined linear operator S in a complex Hilbert space H is subnormal if there exists a normal operator N in a complex Hilbert space K ⊃ H such that S ⊂ N.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 259 - 262
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Bargmann, V., On a Hilbert space of analytic functions and an associated integral transform I, Comm. Pure Appl. Math. 14 (1961), 187–214.CrossRefGoogle Scholar
2.Coddington, E. A., Formally normal operators having no normal extension, Canad. J. Math. 17 (1965), 1030–1040.CrossRefGoogle Scholar
3.Conway, J. B., Subnormal operators (Pitman, 1987).Google Scholar
4.Halmos, P. R., A Hilbert space problem book (Van Nostrand, 1967).Google Scholar
5.Jorgensen, P. E. T., Commutative algebras of unbounded operators, J. Math. Anal. Appl. 122 (1987), 508–527.CrossRefGoogle Scholar
6.Putnam, C. R., Commutation properties of Hilbert space operators and related topics (Springer- Verlag 1967).CrossRefGoogle Scholar
7.Stochel, J. and Szafraniec, F. H., On normal extension of unbounded operators I, J. Operator. Theory 14 (1985), 31–55.Google Scholar
8.Stochel, J. and Szafraniec, F. H., On normal extension of unbounded operators II, Inst. of Math. PAN Preprint 349 (1985).Google Scholar