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A purely analytic criterion for a decomposable operator

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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In [3] E. Bishop introduced the notion of an operator with a “duality theory of type 3” and gave a certain sufficient condition for an operator to have a duality theory of type 3. In this note we show that in fact Bishop's sufficient condition implies that a given operator is decomposable [4]. Moreover, this condition characterizes a decomposable operator.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 1 , January 1980 , pp. 69 - 70
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

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.Apostol, C., Roots of decomposable operator-valued analytic function, Rev. Roumam Math. Pures Appl. 13 (1968), 147–150.Google Scholar
3.Bishop, E., A duality theory for an arbitrary operator, Pacific J. Math. 9 (1959), 379–397.CrossRefGoogle Scholar
4.Foias, C., Spectral maximal spaces and decomposable operators in Banach spaces, Arch Math. (Basel) 14 (1963), 341–349.CrossRefGoogle Scholar
5.Foias, C., On the maximal spectral spaces of a decomposable operator, Rev. Roumain Math. Pures. Appl. 15 (1970), 1599–1606.Google Scholar
6.Frunza, S., A duality theorem for decomposable operators, Rev. Roumaine Math. Pure Appl. 16 (1971), 1055–1058.Google Scholar
7.Radjabalipour, M., Equivalence of decomposable and 2-decomposable operators, Pacific Math., 28 (1978), 243–247CrossRefGoogle Scholar