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The Set of Finite Operators is Nowhere Dense

Published online by Cambridge University Press:  20 November 2018

Domingo A. Herrero*
Affiliation:
Arizona State University Tempe, AZ 85287
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Abstract

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A bounded linear operator A on a complex, separable, infinite dimensional Hilbert space is called finite if for each . It is shown that the class of all finite operators is a closed nowhere dense subset of

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1989

References

1. Ahlfors, L. V., Bounded analytic functions, Duke J. Math. 14 (1947), 111.Google Scholar
2. Anderson, J. H., Derivatives, commutators, and the essential numerical range, Dissertation, Indiana University, 1971.Google Scholar
3. Apostol, C. and B. B. Morrel, On uniform approximation of operators by simple models, Indian Univ. Math. J. 26 (1977), 427442.Google Scholar
4. Brown, A. and C. M. Pearcy, Structure of commutators, Ann. Math. 82 (1965), 112127.Google Scholar
5. Bunce, J. W., Finite operators and amenable C*-algebras, Proc. Amer. Math. Soc. 56 (1976), 145— 151.Google Scholar
6. Davis, C. and P. Rosenthal, Solving linear operator equations, Can. J. Math. 26 (1974), 13841389.Google Scholar
7. Fialkow, L. A. and D. A. Herrero, Finite operators and similarity orbits, Proc. Amer. Math. Soc. 93 (1985), 601609.Google Scholar
8. Herrero, D. A., Approximation of Hilbert space operators. Volume I, Research Notes in Math. 102, Pitman Advanced Books Program, Boston-London-Melbourne, 1982.Google Scholar
9. Herrero, D. A., On quasidiagonal weighted shifts and approximation of operators, Indiana Univ. Math. J. 33 (1984), 549571.Google Scholar
10. Herrero, D. A., What is finite operator? Lecture Notes in Math. 1043 Springer-Verlag, 1984, 240243.Google Scholar
11. Herrero, D. A. and S. J. Szarek, How well can an nx n matrix be approximated by reducible ones? Duke J. Math. 53 (1986), 233248.Google Scholar
12. Kato, T., Perturbation theory for linear operators, Springer-Verlag, 1966.Google Scholar
13. Salinas, N., A characterization of the Browder essential spectrum, Proc. Amer. Math. Soc. 38 (1973), 369373.Google Scholar
14. Voiculescu, D., A non-commutative Weyl-von Neuman theorem, Rev. Roum. Math. Pures et Appl. 21 (1976), 97113.Google Scholar
15. Williams, J. P., Finite operators, Proc. Amer. Math. Soc. 26 (1970), 129136.Google Scholar