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Decomposition algebras of Riesz operators

Published online by Cambridge University Press:  18 May 2009

G. J. Murphy  and
T. T. West
G. J. Murphy
Affiliation:
School of Mathematics, Trinity College, Dublin
T. T. West
Affiliation:
School of Mathematics, Trinity College, Dublin
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Let H be a Hilbert space and let B denote the Banach algebra of all bounded linear operators on H with K denoting the closed ideal of compact operators in B. If T ∈ B, σ(T) and r(T) will denote the spectrum and spectral radius of T, respectively, and π the canonical mapping of B onto the Calkin algebra B/K.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 75 - 79
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

REFERENCES

1.Chui, C. K., Smith, P. W. and Ward, J. D., A note on Riesz operators, Proc. Amer. Math. Soc. 60 (1976), 92–94.CrossRefGoogle Scholar
2.Gillespie, T. A. and West, T. T., A characterisation and two examples of Riesz operators, Glasgow Math. J. 9 (1968), 106–110.Google Scholar
3.Gohberg, I. C. and Kreǐn, M. G., Introduction to the theory of linear nonselfadjoint operators Vol. 18 Translations of Math. Monographs A.M.S. (Providence, 1969).Google Scholar
4.Legg, D., A note on Riesz elements in C*-algebras, Internat. J. Math, and Math. Sci. 1 (1978), 93–96.CrossRefGoogle Scholar
5.Smyth, M. R. F., Riesz theory in Banach algebras, Math. Z. 145 (1975), 145–155.CrossRefGoogle Scholar
6.Smyth, M. R. F., Riesz algebras, Proc. Roy. Irish. Acad. Sect. A 76 (1976), 327–334.Google Scholar
7.Stampfli, J. G., Compact perturbations, normal eigenvalues and a problem of Salinas, J. London Math. Soc. (2), 9 (1974), 165–175.Google Scholar
8.West, T. T., Riesz operators in Banach spaces, Proc. London Math. Soc. (3) 16 (1966), 131–140.CrossRefGoogle Scholar
9.West, T. T., The decomposition of Riesz operators, Proc. London Math. Soc. (3) 16 (1966), 737–752.CrossRefGoogle Scholar
10.Zemánek, J., Spectral radius characterizations of commutativity in Banach algebras. Studia Math. 61 (1977), 257–268.CrossRefGoogle Scholar