Abstract. Let $\lambda_1,\ldots,\lambda_n$ be elements of the essential approximate point spectrum of a bounded Banach space operator. Then there are corresponding approximate eigenvectors $x_1,\ldots,x_n$ such that the norm on the subspace generated by them is almost symmetric. The result can be used in the Scott Brown technique for Banach space operators. Another application is for the local behaviour of operators.

AMS Subject Classification (1991): 47A05, 47A10, 47A15

Received July 1, 1999, and in revised form December 13, 1999. (Registered under 2761/2009.)