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Decomposable Systems of Operators in Harmonic Analysis

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Toeplitz Centennial

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 4))

Abstract

Recently (see [2]), we introduced the notion of decomposability for arbitrary (not necessarily finite) systems of commuting bounded linear operators on a Banach space and extended several results of I. Colojoară, C. Foiaş, Şt. Frunză and the author to this general situation. We now apply this theory to multiplication operators on Banach algebras and study multipliers on Lp (G), 1≤p<∞ for locally compact abelian groups G.

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References

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

    Article  Google Scholar 

  2. Albrecht, E.: Spectral decompositions for systems of commuting operators. To appear in the Proc. Royal Irish Acad.

    Google Scholar 

  3. Apostol, C.: Remarks on the perturbation and a topology for operators. J. Functional Anal. 2 (1968), 395–409.

    Article  Google Scholar 

  4. Apostol, C.: Decomposable multiplication operators. Rev. Roum. Math. Pures Appl. 17 (1972), 323–333.

    Google Scholar 

  5. Bonsall, F.F. and J. Duncan: Complete normed algebras. Springer-Verlag, Berlin-Heidelberg-New York: 1973.

    Book  Google Scholar 

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

    Google Scholar 

  7. Edwards, R.E. and G.I. Gaudry: Littlewood-Paley and multiplier theory. Springer, Berlin-Heidelberg-New York: 1977.

    Book  Google Scholar 

  8. Eschmeier, J.: Operator Decomosability and weakly continuous representations of locally compact abelian groups. Preprint.

    Google Scholar 

  9. Foiaş, C.: Spectral maximal spaces and decomposable operators. Arch, der Math. 14 (1963), 341–349.

    Article  Google Scholar 

  10. Frunză, Şt.: A duality theorem for decomposable operators. Rev. Roum. Math. Pures Appl. 16 (1977), 1055–1058.

    Google Scholar 

  11. Frunză, Şt.: A characterization of regular Banach algebras. Rev. Roum. Math. Pures Appl. 18 (1973), 1057–1059.

    Google Scholar 

  12. Frunză, Şt.: The Taylor spectrum and spectral decompositions. J. Functional Anal. 19 (1975), 390–421.

    Article  Google Scholar 

  13. Hörmander, L.: Estimates for translation invariant operators in Lp spaces. Acta Math. 104 (1960), 93–140.

    Article  Google Scholar 

  14. Rudin, W.: Fourier analysis on groups. Interscience, New York: 1962.

    Google Scholar 

  15. Słodkowski, Z. and W. Zelasko: On joint spectra of commuting families of operators. Studia Math. 50 (1974), 127–148.

    Google Scholar 

  16. Taylor, J.L.: A joint spectrum for several commuting operators. J. Functional Anal. 6 (1970), 172–191.

    Article  Google Scholar 

  17. Taylor, J.L.: The analytic-functional calculus for several commuting operators. Acta Math. 125 (1970), 1–38.

    Article  Google Scholar 

  18. Vasilescu, F.-H.: Calcul funcţional analitic multidimensional. Editura Academiei, Bucureşti: 1979.

    Google Scholar 

  19. Zafran, M.: On the spectra of multipliers. Pacific J. Math. 47 (1973), 609–626.

    Article  Google Scholar 

  20. Zafran, M.: The spectra of multiplier transformations on the Lp spaces. Annals Math. 103 (1976), 355–374.

    Article  Google Scholar 

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© 1982 Springer Basel AG

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Albrecht, E. (1982). Decomposable Systems of Operators in Harmonic Analysis. In: Gohberg, I. (eds) Toeplitz Centennial. Operator Theory: Advances and Applications, vol 4. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5183-1_2

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  • DOI: https://doi.org/10.1007/978-3-0348-5183-1_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5184-8

  • Online ISBN: 978-3-0348-5183-1

  • eBook Packages: Springer Book Archive

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