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A decomposable Hilbert space operator which is not strongly decomposable

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Abstract

In 1978 E. Albrecht constructed a Banach space operator which is decomposable in the sense of C. Foias, but not strongly decomposable. In the present note we describe a method which allows to construct examples of this kind in a systematic and much simpler way. In particular, we exhibit a decomposable, but not strongly decomposable operator on a Hilbert space and thus answer a corresponding question of M.Radjabalipour.

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References

  1. Albrecht,E.: On two questions of I. Colojoarã and C. Foias, Manuscripta Math. 25(1978), 1–15.

    Google Scholar 

  2. Albrecht,E.: On decomposable operators, Integral Equations and Operator Theory 2(1979), 1–10.

    Google Scholar 

  3. Albrecht,E. and Eschmeier, J.: Functional models and local spectral theory, Preprint.

  4. Apostol,C.: Restrictions and quotients of decomposable operators in a Banach space, Rev. Roum. Pures Appl. 13(1968), 147–150.

    Google Scholar 

  5. Bishop,E.: A duality theorem for an arbitrary operator, Pacific J. Math. 9 (1959), 379–394.

    Google Scholar 

  6. Colojoară,I. and Foias, C.: Theory of generalized spectral operators, New York: Gordon and Breach 1968.

    Google Scholar 

  7. Foias,C.: Spectral maximal spaces and decomposable operators in Banach spaces, Arch. Math. 14(1963), 341–349.

    Google Scholar 

  8. Halmos,P.R.: A Hilbert space problem book, Princeton: Van Nostrand 1967.

    Google Scholar 

  9. Köthe,G.: Topologische lineare Räume I, 2. Aufl. Berlin-Heidelberg-New York: Springer-Verlag 1966.

    Google Scholar 

  10. Lang,S.: Real analysis, Reading Massachusetts: Addison-Wesley 1969.

    Google Scholar 

  11. Putinar,M.: Spectral theory and sheaf theory I, Operator Theory: Advances and Applications Vol. 11 (Timisoara and Herculane), 283–297. Basel-Boston-Stuttgart: Birkhäuser Verlag 1983.

    Google Scholar 

  12. Radjabalipour,M.: Decomposable operators, Bull. Iran. Math. Soc. 9(1978), 1–49.

    Google Scholar 

  13. Vasilescu,F.-H.: Analytic functional calculus and spectral decompositions, Bucharest and Dordrecht: Ed. Academiei and D.Reidel Co. 1982.

    Google Scholar 

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Authors and Affiliations

  1. Mathematisches Institut, Universität Münster, Einsteinstraße 62, D-4400, Münster, Federal Republic of Germany

    Jörg Eschmeier

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  1. Jörg Eschmeier
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Eschmeier, J. A decomposable Hilbert space operator which is not strongly decomposable. Integr equ oper theory 11, 161–172 (1988). https://doi.org/10.1007/BF01272116

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  • DOI: https://doi.org/10.1007/BF01272116

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