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Spectral properties of p-hyponormal operators

Published online by Cambridge University Press:  18 May 2009

Muneo Chō
Muneo Chō
Affiliation:
Department of Mathematics, Joetsu University of Education, Joetsu, Nligata 943, Japan
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Let ℋ be a complex Hilbert space and B(ℋ) be the algebra of all bounded linear opeators on ℋ. An operator T ∈ B(ℋ) is said to be p-hyponormal if (T*T)p–(TT*)p. If p = 1, T is hyponormal and if p = ½ is semi-hyponormal. It is well known that a p-hyponormal operator is p-hyponormal for q≤p. Hyponormal operators have been studied by many authors. The semi-hyponormal operator was first introduced by D. Xia in [7]. The p-hyponormal operators have been studied by A. Aluthge in [1]. Let T be a p-hyponormal operator and T=U|T| be a polar decomposition of T. If U is unitary, Aluthge in [1] proved the following properties.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 1 , January 1994 , pp. 117 - 122
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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