Annali di Matematica Pura ed Applicata

, Volume 83, Issue 1, pp 185–194 | Cite as

Commutators of two operators one of which is unbounded and semi-normal

  • Mendel David
Article
  • 29 Downloads

Summary

The concept of semi-normality and hyponormality are defined for unbounded operators in Hilbert Space and Commutators AB-BA, with A unbounded and seminormal and with B bounded, are studied. Four theorems are proved. Two of them are generalizations of results of C. R. Putman.

Keywords

Hilbert Space Unbounded Operator 

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References

  1. [1]
    H. Dunford andJ. Schwartz,Linear operators, Interscience, N.Y., Vol. 1 (1958).Google Scholar
  2. [2]
    C. R. Putnam,On commutators of bounded matrices, Amer. Jour. Math. (1951), pp. 127–131.Google Scholar
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    —— ——,Commutation properties of Hilbert Space operators, Springer Verlag Berlin Heidelberg, New York (1967).Google Scholar
  4. [4]
    F. Riesz andB. Sz. Nagy,Functional Analysis, Frederick Ungar Pnb. Co. N.Y. (1955).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1969

Authors and Affiliations

  • Mendel David

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