Weyl's theorem for a generalized derivation and an elementary operator

Authors

  • B. P. Duggal Department of Mathematics, College of Science, UAEU, P. O. Box 17551, Al Ain, Arab Emirates Author

Keywords:

Weyl's theorem, generalized derivation, elementary operator

Subjects:

47B47, 47B20, 47A53

Abstract

For a,bınB(H), B(H) the algebra of operators on a complex infinite dimensional Hilbert space H, the generalized derivation δabınB(B(H)) and the elementary operator abınB(B(H)) are defined by δab(x)=axxb and ab(x)=axbx. Let dab=δab or ab. It is proved that if a,b are hyponormal, then f(dab) satisfies (generalized) Weyl's theorem for each function f analytic on a neighbourhood of σ(dab).

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Published

2002-10-15