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A characterization of subnormal operators

Published online by Cambridge University Press:  18 May 2009

Alan Lambert
Alan Lambert
Affiliation:
The Weizmann Institute of Science, Rehovot, Israel
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In this note a characterization of subnormality of operators on Hilbert space is given. The characterization is in terms of a sequence of polynomials in the operator and its adjoint reminiscent of the binomial expansion in commutative algebras. As such no external Hilbert spaces are needed, nor is it necessary to introduce forms dependent on arbitrary sequences of vectors from the Hilbert space.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 99 - 101
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Bram, J., Subnormal operators, Duke Math. J., 22 (1955), 75–94.CrossRefGoogle Scholar
2.Embry, M. R., A generalization of the Halmos-Bram criterion for subnormality, Ada Sci. Math. (Szeged), 35 (1973), 61–64.Google Scholar
3.Embry, M. R. and Lambert, A., Weighted translation semigroups, Rocky Mountain J. Math., 7 (1977), 333–344.Google Scholar
4.Embry, M. R. and Lambert, A., Subnormal weighted tranlsation semigroups, J. Functional Analysis 24 (1977), 268–275.Google Scholar
5.Lambert, A., Subnormality and weighted shifts, J. London Math. Soc., (2) 14 (1976), 476–480CrossRefGoogle Scholar
6.Widder, D. W., The Laplace transform, (Princeton Univ. Press, Princeton, N.J., 1946).Google Scholar