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Fredholm theory relative to a Banach algebra homomorphism. (English) Zbl 0479.47032


MSC:

47C05 Linear operators in algebras
47A53 (Semi-) Fredholm operators; index theories
46J05 General theory of commutative topological algebras
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References:

[1] Berberian, S.K.: The Weyl spectrum of an operator. Indiana Univ. J.20, 529-544 (1970) · Zbl 0203.13401 · doi:10.1512/iumj.1970.20.20044
[2] Caradus, S.R., Pfaffenberger, W.E., Yood, B.: Calki algebras and algebras of operators on Banach spaces. New York: Marcel Dekker 1974 · Zbl 0299.46062
[3] Gramsch, B., Lay, D.C.: Spectra mapping theorems for essential spectra. Math. Ann.192, 17-32 (1971) · Zbl 0208.16604 · doi:10.1007/BF02052728
[4] Harte, R.E.: The spectral mapping theorem in several variables. Bull. Amer. Math. Soc.78, 870-874 (1972) · Zbl 0255.47053 · doi:10.1090/S0002-9904-1972-13066-0
[5] Harte, R.E.: Spectra mapping theorems. Proc. Roy. Irish Acad. Sect. A72, 89-107 (1972) · Zbl 0206.13301
[6] Harte, R.E.: The spectral mapping theorem for quasi-commuting systems. Proc. Roy. Irish Acad. Sect. A73, 7-18 (1973) · Zbl 0246.46042
[7] Harte, R.E.: The exponential spectrum in Banach algebras. Proc. Amer. Math. Soc.58, 114-118 (1976) · Zbl 0338.46043 · doi:10.1090/S0002-9939-1976-0407603-5
[8] Harte, R.E., Wickstead, A.W.: Boundaries, hulls and spectral mapping theorems. Proc. Roy. Irish Acad. Sect. A81, 201-208 (1981) · Zbl 0489.46041
[9] Murphy, G.J., West, T.T.: Decomposition of index-zero Fredholm operators. Proc. Roy. Irish Acad. Sect. A81, 49-54 (1981) · Zbl 0474.47007
[10] Smyth, M.R.F.: Riesz algebras. Proc. Roy. Irish Acad. Sect. A76, 327-333 (1976) · Zbl 0345.46040
[11] Snow, M.: A joint Browder essential spectrum. Proc. Roy. Irish Acad. Sect. A75, 129-131 (1975) · Zbl 0326.47002
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