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Lifting sets and the Calkin algebra

Published online by Cambridge University Press:  18 May 2009

G. J. Murphy
G. J. Murphy
Affiliation:
School of Mathematics, Trinity College, Dublin
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H will denote a Hilbert space of infinite dimension, ℬ(H) the algebra of bounded linear operators on H, and ℛ(H) the ideal of compact operators on H. We let σ, σe and σω denote the spectrum, essential spectrum and Weyl spectrum respectively. It is well known that for arbitrary T ∈ ℬ(H) we have by [5]

and

and

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 23 , Issue 1 , January 1982 , pp. 83 - 84
Copyright
Copyright © Glasgow Mathematical Journal Trust 1982

References

REFERENCES

1.Apostol, C., Pearcy, C. and Salinas, N., Spectra of compact perturbations of operators, Indiana Univ. Math. J. 26 (1977), 345–350.CrossRefGoogle Scholar
2.Berger, C. A. and Shaw, B. I., Self-commutators of multi-cyclic hyponormal operators are always trace-class, Bull. Amer. Math. Soc. 79 (1973), 1193–1199.CrossRefGoogle Scholar
3.Caradus, S. R., Pfaffenberger, W. E., Yood, B., Calkin algebras and algebras of operators on Banach spaces, (Marcel Dekker, New York, 1974).Google Scholar
4.Fillmore, P. A., Stampfli, J. G. and Williams, J. P., On the essential numerical range, the essential spectrum, and a problem of Halmos, Ada Sci. Math. (Szeged) 33 (1972), 179–192.Google Scholar
5.Schechter, M.. Invariance of the essential spectrum, Bull. Amer. Math. Soc., 71 (1965), 365–367.CrossRefGoogle Scholar
6.Stampfli, J. G., Compact perturbations, normal eigenvalues and a problem of Salinas. J. London Math. Soc. (2), 9 (1974), 165–175.CrossRefGoogle Scholar
7.West, T. T.. The decomposition of Riesz operators. Proc. London Math. Soc. (3), 16 (1966), 737–752.CrossRefGoogle Scholar