Weakly compact homomorphisms
HTML articles powered by AMS MathViewer
- by J. E. Galé, T. J. Ransford and M. C. White PDF
- Trans. Amer. Math. Soc. 331 (1992), 815-824 Request permission
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.References
- Bernard Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Mathematics, vol. 735, Springer, Berlin, 1979 (French). MR 549769
- Frank F. Bonsall and John Duncan, Complete normed algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 80, Springer-Verlag, New York-Heidelberg, 1973. MR 0423029
- Man Duen Choi and Edward G. Effros, Nuclear $C^*$-algebras and the approximation property, Amer. J. Math. 100 (1978), no. 1, 61–79. MR 482238, DOI 10.2307/2373876
- P. C. Curtis Jr. and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2) 40 (1989), no. 1, 89–104. MR 1028916, DOI 10.1112/jlms/s2-40.1.89
- W. J. Davis, T. Figiel, W. B. Johnson, and A. Pełczyński, Factoring weakly compact operators, J. Functional Analysis 17 (1974), 311–327. MR 0355536, DOI 10.1016/0022-1236(74)90044-5 N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
- José E. Galé, Weakly compact homomorphisms and semigroups in Banach algebras, J. London Math. Soc. (2) 45 (1992), no. 1, 113–125. MR 1157555, DOI 10.1112/jlms/s2-45.1.113 —, Weakly compact homomorphisms between Jordan-Banach algebras, (to appear).
- F. Ghahramani, Compact homomorphisms of $C^*$-algebras, Proc. Amer. Math. Soc. 103 (1988), no. 2, 458–462. MR 943066, DOI 10.1090/S0002-9939-1988-0943066-7
- Barry Edward Johnson, Cohomology in Banach algebras, Memoirs of the American Mathematical Society, No. 127, American Mathematical Society, Providence, R.I., 1972. MR 0374934
- Herbert Kamowitz, Compact endomorphisms of Banach algebras, Pacific J. Math. 89 (1980), no. 2, 313–325. MR 599123
- Herbert Kamowitz and Dennis Wortman, Endomorphisms of an extremal algebra, Proc. Amer. Math. Soc. 104 (1988), no. 3, 852–858. MR 931733, DOI 10.1090/S0002-9939-1988-0931733-0
- Herbert Kamowitz, Stephen Scheinberg, and Dennis Wortman, Compact endomorphisms of Banach algebras. II, Proc. Amer. Math. Soc. 107 (1989), no. 2, 417–421. MR 984801, DOI 10.1090/S0002-9939-1989-0984801-2
- A. A. Kirillov, Elements of the theory of representations, Grundlehren der Mathematischen Wissenschaften, Band 220, Springer-Verlag, Berlin-New York, 1976. Translated from the Russian by Edwin Hewitt. MR 0412321
- Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367
- Lynn H. Loomis, An introduction to abstract harmonic analysis, D. Van Nostrand Co., Inc., Toronto-New York-London, 1953. MR 0054173
- Martin Mathieu, Weakly compact homomorphisms from $C^*$-algebras are of finite rank, Proc. Amer. Math. Soc. 107 (1989), no. 3, 761–762. MR 998737, DOI 10.1090/S0002-9939-1989-0998737-4
- Shûichi Ohno and Junzo Wada, Compact homomorphisms on function algebras, Tokyo J. Math. 4 (1981), no. 1, 105–112. MR 625122, DOI 10.3836/tjm/1270215742
- Gilles Pisier, Factorization of linear operators and geometry of Banach spaces, CBMS Regional Conference Series in Mathematics, vol. 60, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. MR 829919, DOI 10.1090/cbms/060
- Gilles Pisier, Factorization of operators through $L_{p\infty }$ or $L_{p1}$ and noncommutative generalizations, Math. Ann. 276 (1986), no. 1, 105–136. MR 863711, DOI 10.1007/BF01450929
- Shôichirô Sakai, Weakly compact operators on operator algebras, Pacific J. Math. 14 (1964), 659–664. MR 163185
- Joseph L. Taylor, Homology and cohomology for topological algebras, Advances in Math. 9 (1972), 137–182. MR 328624, DOI 10.1016/0001-8708(72)90016-3
Additional Information
- © Copyright 1992 American Mathematical Society
- 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