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2000 | 75 | 2 | 177-192
Tytuł artykułu

On Cohen's proof of the Factorization Theorem

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
Rocznik
Tom
75
Numer
2
Strony
177-192
Opis fizyczny
Daty
wydano
2000
otrzymano
2000-06-28
poprawiono
2000-11-13
Twórcy
  • Faculty of Electrical Engineering, Technical University of Lublin, Nadbystrzycka 38A, P.O. Box 189, 20-618 Lublin, Poland
Bibliografia
  • [A-S] G. R. Allan and A. M. Sinclair, Power factorization in Banach algebras with a bounded approximate identity, Studia Math. 56 (1976), 31-38.
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  • [A;3] M. Altman, Contracteurs dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 274 (1972), 399-400.
  • [A;4] M. Altman, Contractors, approximate identities and factorization in Banach algebras, Pacific J. Math. 48 (1973), 323-334.
  • [A;5] M. Altman, A generalization and the converse of Cohen's factorization theorem, Duke Math. J. 42 (1975), 105-110.
  • [AP] E. Ansari-Piri, A class of factorable topological algebras, Proc. Edinburgh Math. Soc. 33 (1990), 53-59.
  • [B-D] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1979.
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  • [C-S] H. S. Collins and W. H. Summers, Some applications of Hewitt's factorization theorem, Proc. Amer. Math. Soc. 21 (1969), 727-733.
  • [Cr] I. G. Craw, Factorization in Fréchet algebras, J. London Math. Soc. 44 (1969), 607-611.
  • [C-FT] P. C. Curtis, Jr. and A. Figà-Talamanca, Factorization theorems for Banach algebras, in: Function Algebras, F. T. Birtel (ed.), Scott, Foresman and Co., Chicago, IL, 1966, 169-185.
  • [C-St] P. C. Curtis, Jr. and H. Stetkaer, A factorization theorem for anatytic functions operating in a Banach algebra, Pacific J. Math. 37 (1971), 337-343.
  • [D-M] J. Dixmier et P. Malliavin, Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. (2) 102 (1978), 305-330.
  • [D] P. G. Dixon, Automatic continuity of positive functionals on topological involution algebras, Bull. Austral. Math. Soc. 23 (1981), 265-281.
  • [D-W] R. S. Doran and J. Wichmann, Approximate Identities and Factorization in Banach Modules, Lecture Notes in Math. 768, Springer, 1979.
  • [E;I] R. E. Edwards, Fourier Series, a Modern Introduction, Vol. I, 2nd ed., Springer, 1979.
  • [E;II] R. E. Edwards, Fourier Series, a Modern Introduction, Vol. II, 2nd ed., Springer, 1982.
  • [Es;1] J. Esterle, Injection de semi-groupes divisibles dans des algèbres de convolution et construction d'homomorphismes discontinus de C(K), Proc. London Math. Soc. (3) 36 (1978), 59-85.
  • [Es;2] J. Esterle, A complex-variable proof of the Wiener tauberian theorem, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 2, 91-96.
  • [Es;3] J. Esterle, Elements for a classification of commutative radical Banach algebras, in: Proc. Conf. on Radical Banach Algebras and Automatic Continuity (Long Beach, 1981), J. M. Bachar et al. (eds.), Lecture Notes in Math. 975, Springer, Berlin, 1983, 4-65.
  • [Es;4] J. Esterle, Mittag-Leffler method in the theory of Banach algebras and a new approach to Michael's problem, in: Banach Algebras and Several Complex Variables, F. Greenleaf and D. Gulick (eds.), Contemp. Math. 32, Amer. Math. Soc., 1984, 107-129.
  • [F-L] H. G. Feichtinger and M. Leinert, Individual factorization in Banach modules, Colloq. Math. 51 (1987), 107-117.
  • [G-R] J. E. Galé and T. J. Ransford, On the growth of analytic semigroups along vertical lines, Studia Math. 138 (2000), 165-177.
  • [G-W] J. E. Galé and M. C. White, An analytic semigroup version of the Beurling-Helson theorem, Math. Z. 225 (1997), 151-165.
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  • [G-L-R] S. L. Gulick, T. S. Liu and A. C. M. van Rooij, Group algebra modules. II, Canad. J. Math. 19 (1967), 151-173.
  • [H] E. Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964), 147-155.
  • [H-R;II] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Volume II, Structure and Analysis on Compact Groups, Analysis on Locally Compact Abelian Groups, 3rd printing, Springer, 1997.
  • [J] B. E. Johnson, Continuity of centralizers on Banach algebras, J. London Math. Soc. 41 (1966), 639-640.
  • [K] P. Koosis, Sur un théorème de Paul Cohen, C. R. Acad. Sci. Paris 259 (1964), 1380-1382.
  • [K-V] J. Křížková and P. Vrbová, A remark on a factorization theorem, Comment. Math. Univ. Carolin. 15 (1974), 611-614.
  • [L] M. Leinert, A commutative Banach algebra which factorizes but has no approximate units, Proc. Amer. Math. Soc. 55 (1976), 345-346.
  • [Ou] S. I. Ouzomgi, Factorization and automatic continuity for an algebra of infinitely differentiable functions, J. London Math. Soc. (2) 30 (1984), 265-280.
  • [O] J.-L. Ovaert, Factorisation dans les algèbres et modules de convolution, C. R. Acad. Sci. Paris Sér. A 265 (1967), 534-535.
  • [Pal] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Volume I, Algebras and Banach Algebras, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, 1994.
  • [Pas] W. L. Paschke, A factorable Banach algebra without bounded approximate unit, Pacific J. Math. 46 (1973), 249-251.
  • [P-V] H. Petzeltová and P. Vrbová, Factorization in the algebra of rapidly decreasing functions on $R_n$, Comment. Math. Univ. Carolin. 19 (1978), 489-499.
  • [P-P] F. A. Potra and V. Pták, Nondiscrete Induction and Iterative Processes, Res. Notes in Math. 103, Pitman, 1984.
  • [P;1] V. Pták, Un théorème de factorisation, C. R. Acad. Sci. Paris Sér. A 275 (1972), 1297-1299.
  • [P;2] V. Pták, Deux théorèmes de factorisation, ibid. 278 (1974), 1091-1094.
  • [P;3] V. Pták, Factorization in Banach algebras, Studia Math. 65 (1979), 279-285.
  • [Ri] M. Rieffel, On the continuity of certain intertwining operators, centralizers, and positive linear functionals, Proc. Amer. Math. Soc. 20 (1969), 455-457.
  • [R;1] W. Rudin, Factorization in the group algebra of the real line, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 339-340.
  • [R;2] W. Rudin, Representation of functions by convolutions, J. Math. Mech. 7 (1958), 103-115.
  • [S] R. Salem, Sur les transformations des séries de Fourier, Fund. Math. 33 (1939), 108-114.
  • [S-T] F. D. Sentilles and D. C. Taylor, Factorization in Banach algebras and the general strict topology, Trans. Amer. Math. Soc. 142 (1969), 141-152.
  • [S;1] A. M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Funct. Anal. 29 (1978), 308-318.
  • [S;2] A. M. Sinclair, Cohen's factorization method using an algebra of analytic functions, Proc. London Math. Soc. 39 (1979), 451-468.
  • [S;3] A. M. Sinclair, Cohen elements in Banach algebras, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 55-70.
  • [S;4] A. M. Sinclair, Continuous Semigroups in Banach Algebras, London Math. Soc. Lecture Note Ser. 63, Cambridge Univ. Press, 1982.
  • [M.K.S] M. K. Summers, Factorization in Fréchet modules, J. London Math. Soc. (2) 5 (1972), 243-248.
  • [W.H.S] W. H. Summers, Factorization in Fréchet spaces, Studia Math. 39 (1971), 209-216.
  • [T] D. C. Taylor, A characterization of Banach algebras with approximate unit, Bull. Amer. Math. Soc. 74 (1968), 761-766.
  • [V] N. T. Varopoulos, Sur les formes positives d'une algèbre de Banach, C. R. Acad. Sci. Paris Sér. A 258 (1964), 2465-2467.
  • [Vo;1] J. Voigt, Factorization in some Fréchet algebras of differentiable functions, Studia Math. 78 (1984), 333-347.
  • [Vo;2] J. Voigt, Factorization in Fréchet algebras, J. London Math. Soc. (2) 29 (1984), 147-152.
  • [W] M. C. White, Strong Wedderburn decompositions of Banach algebras containing analytic semigroups, J. London Math. Soc. (2) 49 (1994), 331-342.
  • [Z;I] A. Zygmund, Trigonometric Series, Vol. I, 2nd ed., Cambridge Univ. Press, 1959.
  • [Ż] W. Żelazko, Banach Algebras, Elsevier, Amsterdam, and PWN-Polish Sci. Publ., Warszawa, 1973.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv75z2p177bwm
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