Abstract. In this paper, we define a new spectrum (singular spectrum) for a closed operator in a Banach space. The singular spectrum is contained in the classical spectrum and contains the boundary of the latter. We give several characterizations of the points of this new spectrum and show that it has several properties of the classical spectrum. In particular it satisfies the spectral mapping theorem.

AMS Subject Classification (1991): 47A53, 47A55

Keyword(s): Opérateur s-régulier, spectre singulier, conorme, métrique du gap

Received September 23, 1993 and in revised form October 6, 1994. (Registered under 5603/2009.)