Raising bounded groups and splitting of radical extensions of commutative Banach algebras

 Access to full text

 Full (PDF)

1. [AlEr] E. Albrecht and O. Ermert, Commutative nilpotent extensions of commutative C*-algebras split, Bull. London Math. Soc. 29 (1997), 601-608. Zbl0914.46044
2. [BC1] W. G. Bade and P. C. Curtis, Jr., Homomorphisms of commutative Banach algebras, Amer. J. Math. 82 (1960), 589-608. Zbl0093.12503
3. [BC2] W. G. Bade and P. C. Curtis, The Wedderburn decomposition of commutative Banach algebras, ibid., 851-866. Zbl0099.31903
4. [BDL] W. G. Bade, H. G. Dales and Z. A. Lykova, Algebraic and strong splittings of extensions of Banach algebras, Mem. Amer. Math. Soc. 656 (1999). Zbl0931.46034
5. [BD1] F. F. Bonsall and J. Duncan, Complete Normed Algebras, Springer, New York, 1973. Zbl0271.46039
6. [BD2] F. F. Bonsall and J. Duncan, Numerical Ranges of Operators on Normed Spaces and Elements of Normed Algebras, London Math. Soc. Lecture Note Ser. 2, Cambridge Univ. Press, 1971. Zbl0207.44802
7. [BD3] F. F. Bonsall and J. Duncan, Numerical Ranges II, London Math. Soc. Lecture Note Ser. 10, Cambridge Univ. Press, 1973. 
8. [Cu1] P. C. Curtis, Jr., Complementation problems concerning the radical of a commutative amenable Banach algebra, in: Proc. Centre Math. Anal. Austral. Nat. Univ. 21, 1989, 56-60. 
9. [Cu2] P. C. Curtis, Amenability, weak amenability and the close homomorphism property for commutative Banach algebras, in: Function Spaces: The Second Conference, Lecture Notes in Pure and Appl. Math. 172, Marcel Dekker, New York, 1995, 59-69. Zbl0846.46032
10. [Cu1] P. C. Curtis, Jr., and R. J. Loy, The structure of amenable Banach algebras, J. London Math. Soc. (2) 40 (1989), 89-104. 
11. [Da] H. G. Dales, A discontinuous homomorphism from C(X), Amer. J. Math. 101 (1979), 647-734. Zbl0417.46054
12. [Di] P. Dixon, Topologically nilpotent Banach algebras and factorization, Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 329-341. Zbl0762.46039
13. [DS] N. Dunford and J. T. Schwartz, Linear Operators, Part I, Interscience, New York, 1958. 
14. [GL] E. A. Gorin and V. Ya. Lin, On a condition on the radical of a Banach algebra ensuring strong decomposability, Mat. Zametki 2 (1967), 589-592 (in Russian). 
15. [Gr] F. P. Greenleaf, Invariant Means on Topological Groups, Van Nostrand Math. Stud. 16, Van Nostrand, New York, 1969. 
16. [He] A. Ya. Helemskiĭ, Flat Banach modules and amenable algebras, Trudy Moskov. Mat. Obshch. 47 (1984), 179-218 (in Russian); English transl.: Amer. Math. Soc. Transl. 124, 1984, 199-224. 
17. [HP] E. Hille and R. S. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc. Colloq. Publ. 31, Amer. Math. Soc., Providence, 1957. 
18. [Ho] G. Hochschild, On the cohomology theory for associative algebras, Ann. of Math. 46 (1945), 58-76. 
19. [Jo] B. E. Johnson, Cohomology in Banach algebras, Mem. Amer. Math. Soc. 127 (1972). 
20. [Ka] H. Kamowitz, Cohomology groups of commutative Banach algebras, Trans. Amer. Math. Soc. 102 (1962), 352-372. Zbl0114.31703
21. [Lu] G. Lumer, Spectral operators, Hermitian operators and bounded groups, Acta Sci. Math. (Szeged) 25 (1964), 75-85. Zbl0168.12103
22. [P] T. W. Palmer, Banach Algebras and the General Theory of *-Algebras, Volume I: Algebras and Banach Algebras, Encyclopedia Math. Appl. 49, Cambridge Univ. Press, Cambridge, New York, 1994. Zbl0809.46052
23. [Sa] S. Saeki, Helson sets which disobey spectral synthesis, Proc. Amer. Math. Soc. 47 (1975), 371-377. Zbl0297.43007
24. [So1] M. Solovej, Wedderburn decompositions and cohomology for Banach algebras, thesis, Univ. of Leeds, 1993. 
25. [So2] M. Solovej, Wedderburn decompositions of commutative Banach algebras, Proc. Amer. Math. Soc. 123 (1995), 3305-3315. Zbl0844.46027