Geodesic
Generalized Spectral Theory in Complex Banach Algebras
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1211-1236

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

Let A be an element of a complex Banach algebra with identitI. The ordinary spectrum of A, sp(A), consists of those points z in the complex plane such that A — zI has no inverse in . If Q is any other element of , we define spQ (A), the spectrum of A relative to Q, or Q-spectrum of A, as those points z such that has no inverse in . Thus if Q = 0 the Q-spectrum of A is the same as the ordinary spectrum of A.The generalized notion of spectrum, spQ(A), retains many of the properties of the ordinary spectrum, particularly when A and Q commute and the ordinary spectrum of Q does not meet the unit circle. Under these conditions the Q-spectrum of A is a nonempty compact subset of the plane, and if both sp(A) and sp(Q) are finite (or countable), so is spQ (A). 
Hile, G. N.; Pfaffenberger, W. E. Generalized Spectral Theory in Complex Banach Algebras. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1211-1236. doi: 10.4153/CJM-1985-066-3
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