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SOME PROPERTIES OF CLASS A(k) OPERATORS AND THEIR HYPONORMAL TRANSFORMS

Published online by Cambridge University Press:  01 January 2007

J. STELLA IRENE MARY
Affiliation:
Department of Mathematics, PSG college of Arts and Science, Coimbatore-641014, India e-mail: [email protected]@gmail.com
S. PANAYAPPAN
Affiliation:
Department of Mathematics, Goverment Arts collegeCoimbatore-641018, India e-mail: [email protected]
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Abstract.

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In this paper we shall first show that if T is a class A(k) operator then its operator transform is hyponormal. Secondly we prove some spectral properties of T via . Finally we show that T has property (β).

Keywords

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2007

References

REFERENCES

1.Aluthge, A., On p-hyponormal operators for 0< p <1, Int. Eq. 0p. Th. 13 (1990), 307315.CrossRefGoogle Scholar
2.Aluthge, A., Some generalised theorems on p-hyponormal operators, Int. Eq. 0p. Th. 24 (1996), 497501.CrossRefGoogle Scholar
3.Aluthge, A. and Wang, w-hyponormal operators, Int. Eq. 0p. Th. 36 (2000), 110.CrossRefGoogle Scholar
4.Berberian, S. K., A note on hyponormal operators, Pacific J. Math. 12 (1962), 11711175.CrossRefGoogle Scholar
5.Bishop, E., A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), 379397.CrossRefGoogle Scholar
6.Chō, M. and Itoh, M., Putnam's inequality for p-hyponormal operators, Proc. Amer. Math. Soc 123 (1995), 24352440.Google Scholar
7.Chō, M. and Yamazaki, T., An operator transform from class A to the class of hyponormal operators and its application, Int. Eq. 0p. Th. 53 (2005), 497508.CrossRefGoogle Scholar
8.Fujii, M., Jung, D., Lee, S. H., Lee, M. Y. and Nakamoto, R., Some class of operators related to paranormal and log-hyponormal operators, Math. Japan. 51 (2000), 395402.Google Scholar
9.Furuta, T., Ito, M. and Yamazaki, T., A subclass of paranormal operators including class of log-hyponormal and several related classes, Sci. Math. 1 (1998), 389403.Google Scholar
10.Halmos, P. R., Introduction to Hilbert space and the theory of spectral multiplicity (Chelsea, New York, 1951).Google Scholar
11.Huruya, T., A note on p-hyponormal operators, Proc. Amer. Math. Soc. 125 (1997), 36173624.CrossRefGoogle Scholar
12.Ito, M. and Yamazaki, T., Relations between two inequalities and and their applications, Int. Eq. Op. Th. 44 (2002), 442450.CrossRefGoogle Scholar
13.Ito, M. and Yamazaki, T. and Yanagida, M., The polar decomposition of the product of operators and its applications, Int. Eq. Op. Th. 49 (2004), 461472.CrossRefGoogle Scholar
14.Kimura, F., Analysis of non-normal operators via Aluthge transformation, Int. Eq. Op. Th. 50 (2004), 375384.CrossRefGoogle Scholar
15.Putinar, M., Hyponormal operarators are subscalar, J. Operator Theory. 12 (1984), 385395.Google Scholar
16.Stampfli, J., Hyponormal operators, Pacific J. Math. 12 (1962), 14531458.CrossRefGoogle Scholar
17.Xia, D., Spectral theory of hyponormal operators (Birkhauser Verlag, Basel, 1983).CrossRefGoogle Scholar
18.Yamazaki, T., On powers of class A(k) operators including p-hyponormal and log hyponormal operators, Math. Inequal. Appl. 3 (2000), 97104.Google Scholar