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On generalization of decomposability

Published online by Cambridge University Press:  18 May 2009

Ridgley Lange
Ridgley Lange
Affiliation:
Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70122
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Let X be a complex Banach space and let T be a bounded linear operator on X. Then T is decomposable if for every finite open cover of σ(T) there are invariant subspaces Yi(i= 1, 2, …, n) such that

(An invariant subspace Y is spectral maximal [for T] if it contains every invariant subspace Z for which σ(T|Z) ⊂ σ(T|Y).).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 22 , Issue 1 , January 1981 , pp. 77 - 81
Copyright
Copyright © Glasgow Mathematical Journal Trust 1981

References

REFERENCES

1.Albrecht, E., An example of a weakly decomposable operator which is not decomposable, Rev. Roumaine Math. Pures Appl. 20 (1975), 855–861.Google Scholar
2.Albrecht, E., On decomposable operators, Integral Equations and Operator Theory 2 (1979), 1–10.CrossRefGoogle Scholar
3.Apostol, C., Roots of decomposable operator-valued analytic functions, Ren. Roumaine Math. Pures Appl. 13 (1968) 433–438.Google Scholar
4.Erdelyi, I. and Lange, R., Operators with spectral decomposition properties, J. Math. Anal Appl. (to appear).Google Scholar
5.Erdelyi, I and Lange, R., Spectral decompositions on Banach spaces, Lecture Notes in Mathematics No. 623 (Springer-Verlag, 1977).CrossRefGoogle Scholar
6.Finch, J., The single-valued extension property on a Banach space, Pacific J. Math. 58 (1975), 61–69.CrossRefGoogle Scholar
7.Frunzá, S., The single-valued extension property for coinduced operators, Rev. Roumaine Math. Pures Appl. 18 (1973), 1061–1065.Google Scholar
8.Lange, R., Duality and the spectral decomposition property (preprint).Google Scholar