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2000 | 141 | 1 | 85-98
Tytuł artykułu

Raising bounded groups and splitting of radical extensions of commutative Banach algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let A be a commutative unital Banach algebra and let A/ℛ be the quotient algebra of A modulo its radical ℛ. This paper is concerned with raising bounded groups in A/ℛ to bounded groups in the algebra A. The results will be applied to the problem of splitting radical extensions of certain Banach algebras.
Słowa kluczowe
Czasopismo
Rocznik
Tom
141
Numer
1
Strony
85-98
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-12-07
poprawiono
2000-03-17
Twórcy
autor
  • Department of Mathematics University of California Berkeley, CA 94720, U.S.A.
  • Department of Mathematics, University of California, Los Angeles, CA 90024, U.S.A.
  • Department of Mathematics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
Bibliografia
  • [AlEr] E. Albrecht and O. Ermert, Commutative nilpotent extensions of commutative C*-algebras split, Bull. London Math. Soc. 29 (1997), 601-608.
  • [BC1] W. G. Bade and P. C. Curtis, Jr., Homomorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608.
  • [BC2] W. G. Bade and P. C. Curtis, The Wedderburn decomposition of commutative Banach algebras, ibid., 851-866.
  • [BDL] W. G. Bade, H. G. Dales and Z. A. Lykova, Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 656 (1999).
  • [BD1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973.
  • [BD2] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge Univ. Press, 1971.
  • [BD3] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge Univ. Press, 1973.
  • [Cu1] P. C. Curtis, Jr., Complementation problems concerning the radical of a commutative amenable Banach algebra, in: Proc. Centre Math. Anal. Austral. Nat. Univ. 21, 1989, 56-60.
  • [Cu2] P. C. Curtis, Amenability, weak amenability and the close homomorphism property for commutative Banach algebras, in: Function Spaces: The Second Conference, Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, New York, 1995, 59-69.
  • [Cu1] P. C. Curtis, Jr., and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2) 40 (1989), 89-104.
  • [Da] H. G. Dales, A discontinuous homomorphism from C(X), Amer. J. Math. 101 (1979), 647-734.
  • [Di] P. Dixon, Topologically nilpotent Banach algebras and factorization, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329-341.
  • [DS] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958.
  • [GL] E. A. Gorin and V. Ya. Lin, On a condition on the radical of a Banach algebra ensuring strong decomposability, Mat. Zametki 2 (1967), 589-592 (in Russian).
  • [Gr] F. P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand Math. Stud. 16, Van Nostrand, New York, 1969.
  • [He] A. Ya. Helemskiĭ, Flat Banach modules and amenable algebras, Trudy Moskov. Mat. Obshch. 47 (1984), 179-218 (in Russian); English transl.: Amer. Math. Soc. Transl. 124, 1984, 199-224.
  • [HP] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc., Providence, 1957.
  • [Ho] G. Hochschild, On the cohomology theory for associative algebras, Ann. of Math. 46 (1945), 58-76.
  • [Jo] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972).
  • [Ka] H. Kamowitz, Cohomology groups of commutative Banach algebras, Trans. Amer. Math. Soc. 102 (1962), 352-372.
  • [Lu] G. Lumer, Spectral operators, Hermitian operators and bounded groups, Acta Sci. Math. (Szeged) 25 (1964), 75-85.
  • [P] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Volume I: Algebras and Banach Algebras, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, New York, 1994.
  • [Sa] S. Saeki, Helson sets which disobey spectral synthesis, Proc. Amer. Math. Soc. 47 (1975), 371-377.
  • [So1] M. Solovej, Wedderburn decompositions and cohomology for Banach algebras, thesis, Univ. of Leeds, 1993.
  • [So2] M. Solovej, Wedderburn decompositions of commutative Banach algebras, Proc. Amer. Math. Soc. 123 (1995), 3305-3315.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-smv141i1p85bwm
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