On Cohen's proof of the Factorization Theorem
Annales Polonici Mathematici (2000)
- Volume: 75, Issue: 2, page 177-192
- ISSN: 0066-2216
Access Full Article
topAbstract
topHow to cite
topKisyński, Jan. "On Cohen's proof of the Factorization Theorem." Annales Polonici Mathematici 75.2 (2000): 177-192. <http://eudml.org/doc/208393>.
@article{Kisyński2000,
abstract = {Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.},
author = {Kisyński, Jan},
journal = {Annales Polonici Mathematici},
keywords = {factorization for a representation of a Banach algebra with a bounded approximate identity; factorization theorem; representation},
language = {eng},
number = {2},
pages = {177-192},
title = {On Cohen's proof of the Factorization Theorem},
url = {http://eudml.org/doc/208393},
volume = {75},
year = {2000},
}
TY - JOUR
AU - Kisyński, Jan
TI - On Cohen's proof of the Factorization Theorem
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 2
SP - 177
EP - 192
AB - Various proofs of the Factorization Theorem for representations of Banach algebras are compared with its original proof due to P. Cohen.
LA - eng
KW - factorization for a representation of a Banach algebra with a bounded approximate identity; factorization theorem; representation
UR - http://eudml.org/doc/208393
ER -
References
top- [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. Zbl0338.46044
- [A;1] M. Altman, Factorisation dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 272 (1971), 1388-1389. Zbl0232.46045
- [A;2] M. Altman, Infinite products and factorization in Banach algebras, Boll. Un. Mat. Ital. 5 (1972), 217-229. Zbl0252.46043
- [A;3] M. Altman, Contracteurs dans les algèbres de Banach, C. R. Acad. Sci. Paris Sér. A 274 (1972), 399-400. Zbl0232.46044
- [A;4] M. Altman, Contractors, approximate identities and factorization in Banach algebras, Pacific J. Math. 48 (1973), 323-334. Zbl0281.46044
- [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. Zbl0699.46027
- [B-D] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, 1979.
- [C] P. Cohen, Factorization in group algebras, Duke Math. J. 26 (1959), 199-205. Zbl0085.10201
- [C-S] H. S. Collins and W. H. Summers, Some applications of Hewitt's factorization theorem, Proc. Amer. Math. Soc. 21 (1969), 727-733. Zbl0174.18501
- [Cr] I. G. Craw, Factorization in Fréchet algebras, J. London Math. Soc. 44 (1969), 607-611. Zbl0175.14204
- [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. Zbl0203.44702
- [D-M] J. Dixmier et P. Malliavin, Factorisations de fonctions et de vecteurs indéfiniment différentiables, Bull. Sci. Math. (2) 102 (1978), 305-330. Zbl0392.43013
- [D] P. G. Dixon, Automatic continuity of positive functionals on topological involution algebras, Bull. Austral. Math. Soc. 23 (1981), 265-281. Zbl0453.46046
- [D-W] R. S. Doran and J. Wichmann, Approximate Identities and Factorization in Banach Modules, Lecture Notes in Math. 768, Springer, 1979. Zbl0418.46039
- [E;I] R. E. Edwards, Fourier Series, a Modern Introduction, Vol. I, 2nd ed., Springer, 1979. Zbl0424.42001
- [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. Zbl0411.46039
- [Es;2] J. Esterle, A complex-variable proof of the Wiener tauberian theorem, Ann. Inst. Fourier (Grenoble) 30 (1980), no. 2, 91-96. Zbl0419.40005
- [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. Zbl0628.46051
- [G-R] J. E. Galé and T. J. Ransford, On the growth of analytic semigroups along vertical lines, Studia Math. 138 (2000), 165-177. Zbl0959.47024
- [G-W] J. E. Galé and M. C. White, An analytic semigroup version of the Beurling-Helson theorem, Math. Z. 225 (1997), 151-165. Zbl0874.46031
- [G] N. Grønbæk, Power factorization in Banach modules over commutative radical Banach algebras, Math. Scand. 50 (1982), 123-134. Zbl0501.46042
- [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. Zbl0148.12004
- [H] E. Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964), 147-155. Zbl0135.36002
- [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. Zbl0143.36103
- [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. Zbl0329.46055
- [L] M. Leinert, A commutative Banach algebra which factorizes but has no approximate units, Proc. Amer. Math. Soc. 55 (1976), 345-346. Zbl0325.46057
- [Ou] S. I. Ouzomgi, Factorization and automatic continuity for an algebra of infinitely differentiable functions, J. London Math. Soc. (2) 30 (1984), 265-280. Zbl0584.46037
- [O] J.-L. Ovaert, Factorisation dans les algèbres et modules de convolution, C. R. Acad. Sci. Paris Sér. A 265 (1967), 534-535. Zbl0175.14203
- [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. Zbl0257.46050
- [P-V] H. Petzeltová and P. Vrbová, Factorization in the algebra of rapidly decreasing functions on , Comment. Math. Univ. Carolin. 19 (1978), 489-499. Zbl0382.46014
- [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. Zbl0252.46044
- [P;2] V. Pták, Deux théorèmes de factorisation, ibid. 278 (1974), 1091-1094. Zbl0277.46047
- [P;3] V. Pták, Factorization in Banach algebras, Studia Math. 65 (1979), 279-285. Zbl0342.46036
- [Ri] M. Rieffel, On the continuity of certain intertwining operators, centralizers, and positive linear functionals, Proc. Amer. Math. Soc. 20 (1969), 455-457. Zbl0177.41301
- [R;1] W. Rudin, Factorization in the group algebra of the real line, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 339-340. Zbl0079.13301
- [R;2] W. Rudin, Representation of functions by convolutions, J. Math. Mech. 7 (1958), 103-115. Zbl0079.13302
- [S] R. Salem, Sur les transformations des séries de Fourier, Fund. Math. 33 (1939), 108-114. Zbl65.1203.01
- [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. Zbl0185.21103
- [S;1] A. M. Sinclair, Bounded approximate identities, factorization, and a convolution algebra, J. Funct. Anal. 29 (1978), 308-318. Zbl0385.46030
- [S;2] A. M. Sinclair, Cohen's factorization method using an algebra of analytic functions, Proc. London Math. Soc. 39 (1979), 451-468. Zbl0425.46036
- [S;3] A. M. Sinclair, Cohen elements in Banach algebras, Proc. Roy. Soc. Edinburgh Sect. A 84 (1979), 55-70. Zbl0425.46038
- [S;4] A. M. Sinclair, Continuous Semigroups in Banach Algebras, London Math. Soc. Lecture Note Ser. 63, Cambridge Univ. Press, 1982. Zbl0493.46042
- [M.K.S] M. K. Summers, Factorization in Fréchet modules, J. London Math. Soc. (2) 5 (1972), 243-248. Zbl0239.46043
- [W.H.S] W. H. Summers, Factorization in Fréchet spaces, Studia Math. 39 (1971), 209-216. Zbl0214.13703
- [T] D. C. Taylor, A characterization of Banach algebras with approximate unit, Bull. Amer. Math. Soc. 74 (1968), 761-766. Zbl0164.44601
- [V] N. T. Varopoulos, Sur les formes positives d'une algèbre de Banach, C. R. Acad. Sci. Paris Sér. A 258 (1964), 2465-2467. Zbl0131.33103
- [Vo;1] J. Voigt, Factorization in some Fréchet algebras of differentiable functions, Studia Math. 78 (1984), 333-347. Zbl0491.46034
- [Vo;2] J. Voigt, Factorization in Fréchet algebras, J. London Math. Soc. (2) 29 (1984), 147-152. Zbl0569.46028
- [W] M. C. White, Strong Wedderburn decompositions of Banach algebras containing analytic semigroups, J. London Math. Soc. (2) 49 (1994), 331-342. Zbl0833.46047
- [Z;I] A. Zygmund, Trigonometric Series, Vol. I, 2nd ed., Cambridge Univ. Press, 1959. Zbl0085.05601
- [Ż] W. Żelazko, Banach Algebras, Elsevier, Amsterdam, and PWN-Polish Sci. Publ., Warszawa, 1973.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.