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Weakly compact homomorphisms


Authors: J. E. Galé, T. J. Ransford and M. C. White
Journal: Trans. Amer. Math. Soc. 331 (1992), 815-824
MSC: Primary 46H20; Secondary 43A22, 46L05
DOI: https://doi.org/10.1090/S0002-9947-1992-1085942-9
MathSciNet review: 1085942
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Abstract: We study the structure of weakly compact homomorphisms between Banach algebras. In particular, it is shown that between many pairs of algebras, the only weakly compact homomorphisms are those of finite rank.


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  • [1] B. Aupetit, Propriétés spectrales des algères de Banach, Lecture Notes in Math., vol. 735, Springer, Berlin, 1979. MR 549769 (81i:46055)
  • [2] F. F. Bonsall and J. Duncan, Complete normed algebras, Springer, Berlin, 1973. MR 0423029 (54:11013)
  • [3] M. D. Choi and E. G. Effros, Nuclear $ {C^{\ast} }$-algebras and the approximation property, Amer. J. Math. 100 (1978), 61-80. MR 0482238 (58:2317)
  • [4] P. C. Curtis and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2)40 (1989), 89-104. MR 1028916 (90k:46114)
  • [5] W. J. Davis, T. Figiel, W. B. Johnson and A. Pelczyńnski, Factoring weakly compact operators, J. Funct. Anal. 17 (1974), 311-327. MR 0355536 (50:8010)
  • [6] N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
  • [7] J. E. Galé, Weakly compact homomorphisms and semigroups in Banach algebras, J. London Math. Soc. (to appear). MR 1157555 (93d:46076)
  • [8] -, Weakly compact homomorphisms between Jordan-Banach algebras, (to appear).
  • [9] F. Ghahramani, Compact homomorphisms of $ {C^{\ast}}$-algebras, Proc. Amer. Math. Soc. 103 (1988), 458-461. MR 943066 (89e:46065)
  • [10] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. No. 127 (1972). MR 0374934 (51:11130)
  • [11] H. Kamowitz, Compact endomorphisms of Banach algebras, Pacific J. Math. 89 (1980), 313-325. MR 599123 (82c:46063)
  • [12] H. Kamowitz and D. Wortman, Endomorphisms of an extremal algebra, Proc. Amer. Math. Soc. 104 (1988), 852-858. MR 931733 (89g:47035)
  • [13] H. Kamowitz, S. Scheinberg and D. Wortman, Compact endomorphisms of Banach algebras. II, Proc. Amer. Math. Soc. 107 (1989), 417-422. MR 984801 (90b:46107)
  • [14] A. A. Kirillov, Elements of the theory of representations, Springer, Berlin, 1976. MR 0412321 (54:447)
  • [15] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. II, Springer, Berlin, 1979. MR 540367 (81c:46001)
  • [16] L. H. Loomis, An introduction to abstract harmonic analysis, Van Nostrand, Princeton, N.J., 1953. MR 0054173 (14:883c)
  • [17] M. Mathieu, Weakly compact homomorphisms from $ {C^{\ast}}$-algebras are of finite rank, Proc. Amer. Math. Soc. 107 (1989), 761-762. MR 998737 (90k:46130)
  • [18] S. Ohno and J. Wada, Compact homomorphisms on function algebras, Tokyo J. Math. 4 (1981), 105-112. MR 625122 (82i:46079)
  • [19] G. Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conf. Ser. in Math., no. 60, Amer. Math. Soc., Providence, R.I., 1986. MR 829919 (88a:47020)
  • [20] -, Factorization of operators through $ {L_{p\infty }}$ or $ {L_{p1}}$ and non-commutative generalizations, Math. Ann. 276 (1986), 105-136. MR 863711 (88f:47013)
  • [21] S. Sakai, Weakly compact operators on operator algebras, Pacific J. Math. 14 (1964), 659-- 664. MR 0163185 (29:488)
  • [22] J. L. Taylor, Homology and cohomology for topological algebras, Adv. in Math. 9 (1972), 137-182. MR 0328624 (48:6966)

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DOI: https://doi.org/10.1090/S0002-9947-1992-1085942-9
Article copyright: © Copyright 1992 American Mathematical Society

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