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Index Theory for Perturbations of Direct Sums of Normal Operators and Weighted Shifts

Published online by Cambridge University Press:  20 November 2018

I. D. Berg*
Affiliation:
University of Illinois at Urbana-Champaign, Urbana, Illinois
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In this paper we consider the construction of a norm-continuous index theory for unitary equivalence up to commutative normality of operators on a separable Jlilhert space, and establish some essentially best possible results in this direction for operators which can be written as direct sums of weighted shifts and normal operators. Indeed, for such operators we establish both a normcontinuous analogue and a norm-continuous extension of the elegant results of L. Brown, R. Douglas and P. Fillmore [4].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Bastian, J. and Harrison, K., Subnormal weighted shifts and asymptotic properties of norma], operators, Proc. Amer. Math. Soc. 42 (1974), 475479.Google Scholar
2. Berg, I. D., An extension of the Weyl-von Neumann Theorem to normal operators, Trans. Amer. Math. Soc. 160 (1971), 365371.Google Scholar
3. Berg, I. D., On approximation of normal operators by weighted shifts, Mich. Math. J. 21 (1974), 377383.Google Scholar
4. Brown, L., Douglas, R. and Fillmore, P., Unitary equivalence modulo the compact operators and extensions of C* algebras, Proceedings of a Conference on Operator Theory Lecture Notes in Mathematics, Vol. 345 (Springer-Verlag, Berlin, 1973), 58128.Google Scholar
5. Deddens, J. and Stampfli, J., On a question of Douglas and Fillmore, Bull. Amer. Math. Soc. 79 (1973), 327329.Google Scholar
6. Halmos, P., Limits of shifts, Acta Sci. Math. Szeged 3/+ (1973), 131139.Google Scholar
7. Pearcy, C. and Salinas, N., Operators with compact self-commutators, Can. J. Math. 26 (1974), 115120.Google Scholar
8. Stampfli, J., Which weighted shifts are subnormal? Pacific J. Math. 17 (1966), 367379.Google Scholar