Geodesic
Idempotents in Complex Banach Algebras
Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 625-630

Voir la notice de l'article provenant de la source Cambridge University Press

The concept of the spectrum of A relative to Q , where A and Q commute and are elements in a complex Banach algebra with identity I, was developed in [1]. A complex number z is in the Q-resolvent set of A if and only if is invertible in otherwise, z is in the Q-spectrum of A, or spectrum of A relative to Q. One result from [1] was the following.THEOREM. Suppose no points in the ordinary spectrum of Q have unit magnitude. Let C be a simple closed rectifiable curve which lies in the Q-resolvent of A, and let * where P is defined asxs • 
Hile, G. N.; Pfaffenberger, W. E. Idempotents in Complex Banach Algebras. Canadian journal of mathematics, Tome 39 (1987) no. 3, pp. 625-630. doi: 10.4153/CJM-1987-030-1
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[1] 1. Hile, G. N. and Pfaffenberger, W. E., Generalized spectral theory in complex Banach algebras, Can. J. Math. 37 (1985), 1211–1236. Google Scholar

[2] 2. Rickart, C. E., General theory of Banach algebras, The University Series in Higher Mathematics (Van Nostrand, Princeton, N.J., 1960). Google Scholar

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