Adjugates in Banach algebras

Harte, Robin; Hernández, Carlos

doi:10.1090/S0002-9939-05-08317-6

Adjugates in Banach algebras
HTML articles powered by AMS MathViewer

by Robin Harte and Carlos Hernández PDF

Proc. Amer. Math. Soc. 134 (2006), 1397-1404 Request permission

Correction: Proc. Amer. Math. Soc. 138 (2010), 3021-3024.

Abstract:

A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.

References

Bernard Aupetit, A primer on spectral theory, Universitext, Springer-Verlag, New York, 1991. MR 1083349, DOI 10.1007/978-1-4612-3048-9
Bernard Aupetit, Propriétés spectrales des algèbres de Banach, Lecture Notes in Mathematics, vol. 735, Springer, Berlin, 1979 (French). MR 549769, DOI 10.1007/BFb0064204
Bernard Aupetit and H. du T. Mouton, Trace and determinant in Banach algebras, Studia Math. 121 (1996), no. 2, 115–136. MR 1418394
Bruce A. Barnes, G. J. Murphy, M. R. F. Smyth, and T. T. West, Riesz and Fredholm theory in Banach algebras, Research Notes in Mathematics, vol. 67, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982. MR 668516
Matej Brešar and Peter emrl, Finite rank elements in semisimple Banach algebras, Studia Math. 128 (1998), no. 3, 287–298. MR 1611128
R.M. Brits, L. Lindeboom and H. Raubenheimer, On ideals of generalized invertible elements in Banach algebras, Proc. Royal Irish Acad. (to appear).
Bhaggy Duggal, Robin Harte, and In Ho Jeon, Polaroid operators and Weyl’s theorem, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1345–1349. MR 2053338, DOI 10.1090/S0002-9939-03-07381-7
Robin Harte, Fredholm, Weyl and Browder theory, Proc. Roy. Irish Acad. Sect. A 85 (1985), no. 2, 151–176. MR 845539
Robin Harte, Regular boundary elements, Proc. Amer. Math. Soc. 99 (1987), no. 2, 328–330. MR 870795, DOI 10.1090/S0002-9939-1987-0870795-5
Robin Harte, Invertibility and singularity for bounded linear operators, Monographs and Textbooks in Pure and Applied Mathematics, vol. 109, Marcel Dekker, Inc., New York, 1988. MR 920812
Robin Harte, On rank one elements, Studia Math. 117 (1995), no. 1, 73–77. MR 1367694, DOI 10.4064/sm-117-1-73-77
Robin Harte, Block diagonalization in Banach algebras, Proc. Amer. Math. Soc. 129 (2001), no. 1, 181–190. MR 1784022, DOI 10.1090/S0002-9939-00-05884-6
R.E. Harte, C. Hernández and E. de Oteyza, Adjugates of commuting block matrices, (preprint).
Robin Harte and Heinrich Raubenheimer, Fredholm, Weyl and Browder theory. III, Proc. Roy. Irish Acad. Sect. A 95 (1995), no. 1, 11–16. MR 1369040
Irving Kaplansky, Regular Banach algebras, J. Indian Math. Soc. (N.S.) 12 (1948), 57–62. MR 29106
J. J. Koliha, A generalized Drazin inverse, Glasgow Math. J. 38 (1996), no. 3, 367–381. MR 1417366, DOI 10.1017/S0017089500031803
Istvan Kovacs, Daniel S. Silver, and Susan G. Williams, Determinants of commuting-block matrices, Amer. Math. Monthly 106 (1999), no. 10, 950–952. MR 1732497, DOI 10.2307/2589750
L. Lindeboom and H. Raubenheimer, On regularities and Fredholm theory, Czechoslovak Math. J. 52(127) (2002), no. 3, 565–574. MR 1923262, DOI 10.1023/A:1021727829750
T. Mouton and H. Raubenheimer, On rank-one and finite elements of Banach algebras, Studia Math. 104 (1993), no. 3, 211–219. MR 1220661, DOI 10.4064/sm-104-3-211-219
Gerard J. Murphy, Fredholm index theory and the trace, Proc. Roy. Irish Acad. Sect. A 94 (1994), no. 2, 161–166. MR 1369029
J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czechoslovak Math. J. 28(103) (1978), no. 4, 656–676. MR 506439, DOI 10.21136/CMJ.1978.101567
M. R. F. Smyth, Riesz theory in Banach algebras, Math. Z. 145 (1975), no. 2, 145–155. MR 394210, DOI 10.1007/BF01214779
Alan W. Tullo, Conditions on Banach algebras which imply finite dimensionality, Proc. Edinburgh Math. Soc. (2) 20 (1976), no. 1, 1–5. MR 415318, DOI 10.1017/S0013091500015698