|
Adjugates in Banach algebras
Authors:
Robin Harte and Carlos Hernández
Journal:
Proc. Amer. Math. Soc. 134 (2006), 1397-1404
MSC (2000):
Primary 46H05; Secondary 15A15
Posted:
October 7, 2005
Correction:
Proc. Amer. Math. Soc. 138 (2010), 3021-3024
MathSciNet review:
2199186
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: A simple formula for the adjugate of a block triangle offers an alternative route to the determinant theory for Banach algebras.
References
- 1.
B. Aupetit, A primer on spectral theory, Springer-Verlag 1991. MR 1083349 (92c:46001)
- 2.
B. Aupetit, Propriétés spectrales des algébres de Banach, Springer-Verlag 1979. MR 0549769 (81i:46055)
- 3.
B. Aupetit and H. du T. Mouton, Trace and determinant in Banach algebras, Studia Math. 121 (1996) 115-136. MR 1418394 (97i:46086)
- 4.
B.A. Barnes, G.J. Murphy, M.R.F. Smyth and T.T. West, Riesz and Fredholm theory in Banach algebras, Pitman 1982. MR 0668516 (84a:46108)
- 5.
M. Bresar and P. Semrl, Finite rank elements in Banach algebras, Studia Math. 128 (1998) 287-298. MR 1611128 (99a:46089)
- 6.
R.M. Brits, L. Lindeboom and H. Raubenheimer, On ideals of generalized invertible elements in Banach algebras, Proc. Royal Irish Acad. (to appear).
- 7.
B.P. Duggal, R.E. Harte and I.H. Jeon, Polaroid operators and Weyl's theorem, Proc. Amer. Math. Soc. 132 (2004) 1345-1349. MR 2053338 (2004m:47005)
- 8.
R.E. Harte, Fredholm, Weyl and Browder theory, Proc. Royal Irish Acad. 85A (1985) 151-176. MR 0845539 (87h:47029)
- 9.
R.E. Harte, Regular boundary elements, Proc. Amer. Math. Soc. 88 (1987) 328-330. MR 0870795 (88d:46088)
- 10.
R.E. Harte, Invertibility and singularity, Dekker 1988. MR 0920812 (89d:47001)
- 11.
R.E. Harte, On rank one elements, Studia Math. 117 (1995) 73-77. MR 1367694 (96i:46055)
- 12.
R.E. Harte, Block diagonalization in Banach algebras, Proc. Amer. Math. Soc. 129 (2001) 181-190. MR 1784022 (2001k:47013)
- 13.
R.E. Harte, C. Hernández and E. de Oteyza, Adjugates of commuting block matrices, (preprint).
- 14.
R.E. Harte and H. Raubenheimer, Fredholm, Weyl and Browder theory III, Proc. Royal Irish Acad. 95A 1995 11-16. MR 1369040 (96i:47002)
- 15.
I. Kaplansky, Regular Banach algebras, Jour. Indian Math. Soc. 12 (1948) 57-62. MR 0029106 (10:549b)
- 16.
J.J. Koliha, A generalized Drazin inverse, Glasgow Math. Jour. 38 (1996) 367-381. MR 1417366 (98b:46065)
- 17.
I. Kovacs, D.S. Silver and S.G. Williams, Determinants for commuting block matrices, Amer. Math. Monthly 106 (1999) 950-952. MR 1732497
- 18.
L. Lindeboom and H. Raubenheimer, On regularities and Fredholm theory, Czech Math. Jour. 52 (2002) 565-574. MR 1923262 (2003h:46070)
- 19.
H. du T. Mouton and H. Raubenheimer, On rank one and finite elements in Banach algebras, Studia Math. 104 (1993) 17-25. MR 1220661 (94c:46095)
- 20.
G.J. Murphy, Fredholm index theory and the trace, Proc. Royal Irish Acad. 94A (1994) 161-166. MR 1369029 (96m:47021)
- 21.
J. Puhl, The trace of finite and nuclear elements in Banach algebras, Czech Math. Jour. 28 (1978) 656-676. MR 0506439 (81a:47024)
- 22.
M.R.F. Smyth, Riesz theory in Banach algebras, Math. Zeit. 45 (1975) 145-155. MR 0394210 (52:15013)
- 23.
A.W. Tullo, Conditions on Banach algebras which imply finite dimensionality, Proc. Edinburgh Math. Soc. 20 (1976) 1-5. MR 0415318 (54:3407)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC (2000):
46H05,
15A15
Retrieve articles in all journals
with MSC (2000):
46H05,
15A15
Additional Information
Robin Harte
Affiliation:
School of Mathematics, Trinity College, Dublin 2, Ireland
Email:
rharte@maths.tcd.ie
Carlos Hernández
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, D.F. 04510, México
Email:
carlosh@servidor.unam.mx
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08317-6
PII:
S 0002-9939(05)08317-6
Keywords:
Banach algebras,
Fredholm theory,
adjugate,
determinant,
socle
Received by editor(s):
December 10, 2004
Posted:
October 7, 2005
Additional Notes:
The first author was supported by Enterprise Ireland Basic Research Grant SC/2002/0266
Communicated by:
David R. Larson
Article copyright:
© Copyright 2005 American Mathematical Society
|
