Sur les algèbres $S$-régulières et la $S$-décomposabilité des opérateurs de multiplication
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- by A. Daoui, H. Mahzouli and E. H. Zerouali PDF
- Proc. Amer. Math. Soc. 131 (2003), 3211-3220 Request permission
Abstract:
Let $A$ be a commutative Banach algebra and $\Delta (A)$ its maximal ideal space. For given $S \subset \Delta (A)$, we establish necessary and sufficient conditions so that $A$ becomes $S$-regular. We derive some characterizations of decomposable multiplication operators and a description of the Apostol algebra of $A$. This provides a class of algebras(including Douglas algebras) for which the Apostol algebra is regular.References
- Ion Colojoară and Ciprian Foiaş, Theory of generalized spectral operators, Mathematics and its Applications, Vol. 9, Gordon and Breach Science Publishers, New York-London-Paris, 1968. MR 0394282
- J. Eschmeier and M. Putinar, On quotients and restrictions of generalized scalar operators, J. Funct. Anal. 84 (1989), no. 1, 115–134. MR 999491, DOI 10.1016/0022-1236(89)90113-4
- Şt. Frunză, A characterization of regular Banach algebras, Rev. Roumaine Math. Pures Appl. 18 (1973), 1057–1059. MR 324419
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- Kenneth Hoffman, Banach spaces of analytic functions, Dover Publications, Inc., New York, 1988. Reprint of the 1962 original. MR 1102893
- H. Mahzouli and E. H. Zerouali, Classes de shifts décomposables sur les espaces de Beurling, Arch. Math. (Basel) 76 (2001), no. 2, 127–132 (French, with English summary). MR 1811290, DOI 10.1007/s000130050552
- Ridgley Lange and Sheng Wang Wang, New approaches in spectral decomposition, Contemporary Mathematics, vol. 128, American Mathematical Society, Providence, RI, 1992. MR 1162741, DOI 10.1090/conm/128
- Ronald Larsen, An introduction to the theory of multipliers, Die Grundlehren der mathematischen Wissenschaften, Band 175, Springer-Verlag, New York-Heidelberg, 1971. MR 0435738
- Kjeld B. Laursen and Michael M. Neumann, An introduction to local spectral theory, London Mathematical Society Monographs. New Series, vol. 20, The Clarendon Press, Oxford University Press, New York, 2000. MR 1747914
- Kjeld B. Laursen and Michael M. Neumann, Decomposable multipliers and applications to harmonic analysis, Studia Math. 101 (1992), no. 2, 193–214. MR 1149572, DOI 10.4064/sm-101-2-193-214
- Kjeld B. Laursen and Michael M. Neumann, Local spectral properties of multipliers on Banach algebras, Arch. Math. (Basel) 58 (1992), no. 4, 368–375. MR 1152625, DOI 10.1007/BF01189927
- B. Nagy, A strong spectral residuum for every closed operator, Illinois J. Math. 24 (1980), no. 2, 173–179. MR 575056
- M. M. Neumann, Commutative Banach algebras and decomposable operators, Monatsh. Math. 113 (1992), no. 3, 227–243. MR 1163303, DOI 10.1007/BF01641770
- Osamu Hatori and Keiji Izuchi, Apostol algebras and decomposition in Douglas algebras, Michigan Math. J. 44 (1997), no. 3, 435–449. MR 1481112, DOI 10.1307/mmj/1029005781
- Raymond Mortini, Decomposable multiplication operators on $H^\infty +C$, Arch. Math. (Basel) 72 (1999), no. 1, 64–67. MR 1657359, DOI 10.1007/s000130050304
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- Florian-Horia Vasilescu, Analytic functional calculus and spectral decompositions, Mathematics and its Applications (East European Series), vol. 1, D. Reidel Publishing Co., Dordrecht; Editura Academiei Republicii Socialiste România, Bucharest, 1982. Translated from the Romanian. MR 690957
Additional Information
- A. Daoui
- Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
- Email: daoui@fsr.ac.ma
- H. Mahzouli
- Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
- Email: houssame.mahzouli@caramail.com
- E. H. Zerouali
- Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
- Email: zerouali@fsr.ac.ma
- Received by editor(s): June 29, 2000
- Received by editor(s) in revised form: May 19, 2002
- Published electronically: February 6, 2003
- Communicated by: David R. Larson
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3211-3220
- MSC (2000): Primary 47B40, 47B48; Secondary 47A11
- DOI: https://doi.org/10.1090/S0002-9939-03-06904-1
- MathSciNet review: 1992862