Multiplier algebras, Banach bundles, and one-parameter semigroups
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 287-322.
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Chojnacki, Wojciech. Multiplier algebras, Banach bundles, and one-parameter semigroups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 287-322. http://www.numdam.org/item/ASNSP_1999_4_28_2_287_0/

[1] M. Altman, Factorisation dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 272 (1971), 1388-1389. | MR | Zbl

[2] M. Altman, A generalization and the converse of Cohen's factorization theorem, Duke Math. J. 42 (1975), 105-110. | MR | Zbl

[3] A. Bobrowski, On the Yosida approximation and the Widder-Arendt representation theorem, Studia Math. 124 (1997), 281-290. | MR | Zbl

[4] F.F. Bonsall - J. Duncan, "Complete Normed Algebras", Springer-Verlag, Berlin, New York, 1973. | MR | Zbl

[5] W. Chojnacki, On the equivalence of a theorem of Kisyński and the Hille-Yosida generation theorem, Proc. Amer. Math. Soc. 126 (1998), 491-497. | MR | Zbl

[6] W. Chojnacki - J. Kisy, On the Favard classes of semigroups associated with pseudo-resolvents, Acta Sci. Math. (Szeged) 64 (1998), 681-696. | MR | Zbl

[7] P.J. Cohen, Factorization in group algebras, Duke Math. J. 26 (1959), 199-205. | MR | Zbl

[8] P.C. Curtis, JR. - A. Figá-Talamanca, Factorization theorems for Banach algebras, In: "Function Algebras" (Frank T. Birtel, ed.), Scott, Foresman and Co., Chicago, Ill., 1966, pp. 169-185. | MR | Zbl

[9] C. Dellacherie - P.A. Meyer, "Probabilities and potential C", North-Holland, Amsterdam, New York, 1988. | MR | Zbl

[10] M Despić - F. Ghahramani - S. Grabiner, Weighted convolution algebras without bounded approximate identities, Math. Scand. 76 (1995), 257-272. | MR | Zbl

[11] R.S. Doran - J. Wichmann, "Approximate identities and factorization in Banach modules", Lecture Notes in Math., vol. 768, Springer-Verlag, Berlin, Heidelberg, New York, 1979. | MR | Zbl

[12] A. Douady - L. Dal Soglio-Hérault, Existence de sections pour un fibré de Banach au sens de Fell, unpublished manuscript (see also Appendix in [15] and Appendix D in [16]).

[13] M.J. Dupré - R.M. Gillette, "Banach bundles, Banach modules and automorphisms of C*-algebras", Pitman, Boston, London, Melbourne, 1983. | MR | Zbl

[14] J.M.G. Fell, The structure of algebras of operator fields, Acta Math. 106 (1961), 233-280. | MR | Zbl

[15] J.M.G. Fell, "Induced representations and Banach *-algebraic bundles", Lecture Notes in Math., vol. 582, Springer-Verlag, Berlin, Heidelberg, New York, 1977. | MR | Zbl

[16] J.M.G. Fell - R. S. DORAN" "Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles", Academic Press, Boston, 1988. | Zbl

[17] F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc. (2) 21 (1980), 149-161. | MR | Zbl

[18] S. Grabiner, Homomorphisms and semigroups in weighted convolution algebras, Indiana Univ. Math. J. 37 (1988), 589-615. | MR | Zbl

[19] S.L. Gulick - T.S. Liu - A.C.M. Van Rooij, Group algebra modules. II, Canad. J. Math. 19 (1967), 151-173. | MR | Zbl

[20] E. Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964), 147-155. | MR | Zbl

[21] K.H. Hofmann, Representations of algebras by continuous sections, Bull. Amer. Math. Soc. (N.S.) 78 (1972), 291-373. | MR | Zbl

[22] K.H. Hofmann, "Banach bundles", Darmstadt Notes, 1974.

[23] K.H. Hofmann, Bundles and sheaves are equivalent in the category of Banach spaces, In: "K-theory and operator algebras: proceedings of a conference held at the University of Georgia in Athens, Georgia, April 21-25, 1975" (B. B. Morrel and I. M. Singer, eds.), Lecture Notes in Math., vol. 575, Springer-Verlag, Berlin, Heidelberg, New York, 1977, pp. 53-69. | MR | Zbl

[24] B.E. Johnson, Centralisers on certain topological algebras, J. London Math. Soc. 39 (1964), 603-614. | MR | Zbl

[25] B.E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc. (3) 14 (1964), 299-320. | MR | Zbl

[26] J Kisyński, personal communication.

[27] J Kisyński, The Widder spaces, representations of the convolution algebra L1 (R+), and one parameter semigroups of operators, Preprint no. 588, Institute of Mathematics, Polish Academy of Sciences, Warsaw, June 1998.

[28] P. Koosis, Sur un théorème de Paul Cohen, C. R. Acad. Sci. Paris 259 (1964), 1380-1382. | MR | Zbl

[29] T.G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375. | MR | Zbl

[30] T.G. Kurtz, A general theorem on the convergence of operator semigroups, Trans. Amer. Math. Soc. 148 (1970), 23-32. | MR | Zbl

[31] T.W. Palmer, "Banach Algebras and The General Theory of *-Algebras, Volume I: Algebras and Banach Algebras", Encyclopedia of Mathematics and Its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. | Zbl

[32] F.A. Potra - V. Pták, "Nondiscrete induction and iterative processes", Research Notes in Math., vol. 103, Pitman (Advance Publishing Program), Boston, Mass., 1984. | MR | Zbl

[33] V. Pták, Un théorème de factorisation, C. R. Acad. Sci. Paris Sér. A 275 (1972), 1297-1299. | MR | Zbl

[34] V. Pták, Deux théorèmes de factorisation, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1091-1094. | MR | Zbl

[35] V. Pták, Factorization in Banach algebras, Studia Math. 65 (1979), 279-285. | EuDML | MR | Zbl

[36] D. Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43-72. | MR | Zbl

[37] I.E. Segal - R.A. Kunze, "Integrals and operators", 2 ed., Springer-Verlag, Berlin, 1978. | MR | Zbl

[38] A.M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Funct. Anal. 29 (1978), 308-318. | MR | Zbl

[39] A.M. Sinclair, Cohen elements in Banach algebras, Proc. Roy. Soc. Edinburgh Sec. A 84 (1979), 55-70. | MR | Zbl

[40] A.M. Sinclair, Cohen's factorization method using an algebra of analytic functions, Proc. London Math. Soc. (3) 39 (1979), 451-468. | MR | Zbl

[41] A.M. Sinclair, "Continuous semigroups in Banach algebras", Cambridge University Press, Cambridge, New York, 1982. | MR | Zbl

[42] H.F. Trotter, Approximation of semigroups of operators, Pacific J. Math. 8 (1958), 887-919. | MR | Zbl

[43] J.G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math. 2 (1952), 251-261. | MR | Zbl

[44] G.A. Willis, The continuity of derivations and module homomorphisms, J. Austral. Math. Soc. Ser. A 40 (1986), 299-320. | MR | Zbl