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Title

Multipliers and local spectral theory

Authors 1

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  1. Matematisk Institut, Kοbenhavns Universitet, Universitetsparken 5, DK-2100 Kοbenhavn Ø, Denmark

Bibliography

  1. [AL] P. Aiena and K. B. Laursen, Multipliers with closed range on regular commutative Banach algebras, Proc. Amer. Math. Soc., to appear.
  2. [A1] E. Albrecht, Decomposable systems of operators in harmonic analysis, in: Toeplitz Centennial, Birkhäuser, Basel, 1982, 19-35.
  3. [A2] E. Albrecht, Spectral decompositions for systems of commuting operators, Proc. Roy. Irish Acad. 81A (1981), 81-98.
  4. [Ap] C. Apostol, Decomposable multiplication operators, Rev. Roumaine Math. Pures Appl. 17 (1972), 323-333.
  5. [BD] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973.
  6. [CF] I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
  7. [C] J. B. Conway, A Course in Functional Analysis, Springer, New York, 1985.
  8. [DT] M. Dutta and U. B. Tewari, On multipliers of Segal algebras, Proc. Amer. Math. Soc. 72 (1978), 121-124.
  9. [E] J. Eschmeier, Spectral decompositions and decomposable multipliers, Manuscripta Math. 51 (1985), 201-224.
  10. [ELN] J. Eschmeier, K. B. Laursen and M. M. Neumann, Multipliers with natural local spectra on commutative Banach algebras, submitted.
  11. [F] K.-H. Förster, Über die Invarianz einiger Räume, die zum Operator T - λA gehören, Arch. Math. (Basel) 17 (1966), 56-64.
  12. [Fr] Şt. Frunză, A characterization of regular Banach algebras, Rev. Roumaine Math. Pures Appl. 18 (1973), 1057-1059.
  13. [G] I. Glicksberg, When is μ*L₁ closed?, Trans. Amer. Math. Soc. 160 (1971), 419-425.
  14. [GK] M. A. Gol'dman and S. N. Kračkovskiĭ, Invariance of certain spaces connected with the operator A - λI, Soviet Math. Dokl. 5 (1964), 102-104.
  15. [GMcG] C. C. Graham and O. C. McGehee, Essays in Commutative Harmonic Analysis, Springer, New York, 1979.
  16. [H] H. Helson, Isomorphisms of abelian group algebras, Ark. Mat. 2 (1953), 475-487.
  17. [HP] B. Host et F. Parreau, Sur un problème de I. Glicksberg: Les idéaux fermés de type fini de M(G), Ann. Inst. Fourier (Grenoble) 28 (3) (1978), 143-164.
  18. [K] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Analyse Math. 6 (1958), 261-322.
  19. [L] R. Larsen, An Introduction to the Theory of Multipliers, Springer, New York, 1971.
  20. [LN1] K. B. Laursen and M. M. Neumann, Decomposable multipliers and applications to harmonic analysis, Studia Math. 101 (1992), 193-214.
  21. [LN2] K. B. Laursen and M. M. Neumann, Local spectral theory and spectral inclusions, Glasgow Math. J., to appear.
  22. [LV1] K. B. Laursen and P. Vrbová, Some remarks on the surjectivity spectrum of linear operators, Czechoslovak Math. J. 39 (1989), 730-739.
  23. [LV2] K. B. Laursen and P. Vrbová, Intertwiners and automatic continuity, J. London Math. Soc. (2) 43 (1991), 149-155.
  24. [M] M. Mbekhta, Résolvant généralisé et théorie spectrale, J. Operator Theory 21 (1989), 69-105.
  25. [MN] V. G. Miller and M. M. Neumann, Local spectral theory for multipliers and convolution operators, in: Proceedings of the Great Plains Operator Symposium at Iowa City, Birkhäuser, Basel, to appear.
  26. [N] M. M. Neumann, Commutative Banach algebras and decomposable operators, Monatsh. Math. 113 (1992), 227-243.
  27. [PV] V. Pták and P. Vrbová, Algebraic spectral subspaces, Czechoslovak Math. J. 38 (1988), 173-179.
  28. [RW] L. T. Ramsey and B. B. Wells, Jr., Some results on the question: When is μ*L¹ closed?, Indiana Univ. Math. J. 26 (1977), 987-996.
  29. [S] C. Schmoeger, Ein Spektralabbildungssatz, Arch. Math. (Basel) 55 (1990), 484-489.
  30. [SW] M. Ó Searcóid and T. T. West, Continuity of the generalized kernel and range of semi-Fredholm operators, Math. Proc. Cambridge Philos. Soc. 105 (1989), 513-522.
  31. [V1] F.-H. Vasilescu, Residually decomposable operators in Banach spaces, Tôhoku Math. J. 21 (1969), 509-522.
  32. [V2] F.-H. Vasilescu, Analytic Functional Calculus, Reidel, Dordrecht, 1982.
  33. [W] J. G. Wendel, On isometric isomorphism of group algebras, Pacific J. Math. 1 (1951), 305-311.
  34. [Z] M. Zafran, On the spectra of multipliers, ibid. 47 (1973), 609-626.
Banach Center Publications
1994/30/1
Export to PBN, Opens in new tab
Pages:
223-236
Main language of publication
English
Published
1994
Exact and natural sciences