Multiplier algebras, Banach bundles, and one-parameter semigroups

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1. [1] M. Altman, Factorisation dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A272 (1971), 1388-1389. Zbl0232.46045MR284814
2. [2] M. Altman, A generalization and the converse of Cohen's factorization theorem, Duke Math. J.42 (1975), 105-110. Zbl0347.46049MR394207
3. [3] A. Bobrowski, On the Yosida approximation and the Widder-Arendt representation theorem, Studia Math.124 (1997), 281-290. Zbl0876.44001MR1456426
4. [4] F.F. Bonsall - J. Duncan, "Complete Normed Algebras", Springer-Verlag, Berlin, New York, 1973. Zbl0271.46039MR423029
5. [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. Zbl0893.46044MR1415577
6. [6] W. Chojnacki - J. Kisy, On the Favard classes of semigroups associated with pseudo-resolvents, Acta Sci. Math. (Szeged) 64 (1998), 681-696. Zbl0937.47044MR1666075
7. [7] P.J. Cohen, Factorization in group algebras, Duke Math. J.26 (1959), 199-205. Zbl0085.10201MR104982
8. [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. Zbl0191.13802MR203500
9. [9] C. Dellacherie - P.A. Meyer, "Probabilities and potential C", North-Holland, Amsterdam, New York, 1988. Zbl0716.60001MR939365
10. [10] M Despić - F. Ghahramani - S. Grabiner, Weighted convolution algebras without bounded approximate identities, Math. Scand.76 (1995), 257-272. Zbl0849.46035MR1354583
11. [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. Zbl0418.46039MR555240
12. [12] A. Douady - L. Dal Soglio-Hérault, Existence de sections pour un fibré de Banach au sens de Fell, unpublished manuscript (see also Appendix in [15] and Appendix D in [16]). 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. [13] M.J. Dupré - R.M. Gillette, "Banach bundles, Banach modules and automorphisms of C*-algebras", Pitman, Boston, London, Melbourne, 1983. Zbl0536.46048MR721812
14. [14] J.M.G. Fell, The structure of algebras of operator fields, Acta Math.106 (1961), 233-280. Zbl0101.09301MR164248
15. [15] J.M.G. Fell, "Induced representations and Banach *-algebraic bundles", Lecture Notes in Math., vol. 582, Springer-Verlag, Berlin, Heidelberg, New York, 1977. Zbl0372.22001MR457620
16. [16] J.M.G. Fell - R. S. DORAN" "Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles", Academic Press, Boston, 1988. Zbl0652.46050
17. [17] F. Ghahramani, Homomorphisms and derivations on weighted convolution algebras, J. London Math. Soc. (2) 21 (1980), 149-161. Zbl0435.43005MR576191
18. [18] S. Grabiner, Homomorphisms and semigroups in weighted convolution algebras, Indiana Univ. Math. J.37 (1988), 589-615. Zbl0676.46037MR962925
19. [19] S.L. Gulick - T.S. Liu - A.C.M. Van Rooij, Group algebra modules. II, Canad. J. Math.19 (1967), 151-173. Zbl0148.12004MR222663
20. [20] E. Hewitt, The ranges of certain convolution operators, Math. Scand.15 (1964), 147-155. Zbl0135.36002MR187016
21. [21] K.H. Hofmann, Representations of algebras by continuous sections, Bull. Amer. Math. Soc. (N.S.) 78 (1972), 291-373. Zbl0237.16018MR347915
22. [22] K.H. Hofmann, "Banach bundles", Darmstadt Notes, 1974. 
23. [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. Zbl0346.46053MR487491
24. [24] B.E. Johnson, Centralisers on certain topological algebras, J. London Math. Soc.39 (1964), 603-614. Zbl0124.06902MR167849
25. [25] B.E. Johnson, An introduction to the theory of centralizers, Proc. London Math. Soc. (3) 14 (1964), 299-320. Zbl0143.36102MR159233
26. [26] J Kisyński, personal communication. 
27. [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. [28] P. Koosis, Sur un théorème de Paul Cohen, C. R. Acad. Sci. Paris259 (1964), 1380-1382. Zbl0175.14202MR172069
29. [29] T.G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal.3 (1969), 354-375. Zbl0174.18401MR242016
30. [30] T.G. Kurtz, A general theorem on the convergence of operator semigroups, Trans. Amer. Math. Soc.148 (1970), 23-32. Zbl0194.44103MR256210
31. [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. Zbl0809.46052
32. [32] F.A. Potra - V. Pták, "Nondiscrete induction and iterative processes", Research Notes in Math., vol. 103, Pitman (Advance Publishing Program), Boston, Mass., 1984. Zbl0549.41001MR754338
33. [33] V. Pták, Un théorème de factorisation, C. R. Acad. Sci. Paris Sér. A275 (1972), 1297-1299. Zbl0252.46044MR312269
34. [34] V. Pták, Deux théorèmes de factorisation, C. R. Acad. Sci. Paris Sér. A278 (1974), 1091-1094. Zbl0277.46047MR341096
35. [35] V. Pták, Factorization in Banach algebras, Studia Math.65 (1979), 279-285. Zbl0342.46036MR567080
36. [36] D. Ray, Resolvents, transition functions, and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43-72. Zbl0092.34501MR107302
37. [37] I.E. Segal - R.A. Kunze, "Integrals and operators", 2 ed., Springer-Verlag, Berlin, 1978. Zbl0373.28001MR486380
38. [38] A.M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Funct. Anal.29 (1978), 308-318. Zbl0385.46030MR512247
39. [39] A.M. Sinclair, Cohen elements in Banach algebras, Proc. Roy. Soc. Edinburgh Sec.A84 (1979), 55-70. Zbl0425.46038MR549871
40. [40] A.M. Sinclair, Cohen's factorization method using an algebra of analytic functions, Proc. London Math. Soc. (3) 39 (1979), 451-468. Zbl0425.46036MR550079
41. [41] A.M. Sinclair, "Continuous semigroups in Banach algebras", Cambridge University Press, Cambridge, New York, 1982. Zbl0493.46042MR664431
42. [42] H.F. Trotter, Approximation of semigroups of operators, Pacific J. Math.8 (1958), 887-919. Zbl0099.10302MR103420
43. [43] J.G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math.2 (1952), 251-261. Zbl0049.35702MR49911
44. [44] G.A. Willis, The continuity of derivations and module homomorphisms, J. Austral. Math. Soc. Ser. A40 (1986), 299-320. Zbl0626.43004MR832972

1. Jan Kisyński, Around Widder’s characterization of the Laplace transform of an element of $L^{\infty }\left({ℝ}^{+}\right)$