Errata, volume 16; Errata, volume 17; Errata, volume 18

1967 Proceedings of the American Mathematical Society  
approximation theorem for a class of operators, pp. 991-995. It has been pointed out to the author by Y. Domar that Theorem 2 of the author's paper [2] is not correct as stated. In this note the correct form of the theorem is given together with a brief sketch of the proof. The theorem is a generalization of an approximation theorem for unitary operators in Hilbert space to certain classes of operators in Banach spaces. The class is defined by the following restrictions. Let V be any bounded
more » ... ertible operator in a Banach space B which satisfies the following two conditions. (i) || Vn\\ =0(\ n\ Q) as \n\ tends to infinity for some positive integer a. (ii) lim inf|"|^M||Fn]||w|-5 = 0. If V satisfies these conditions, then the correct version of Theorem 2 is as follows. Theorem 2. Given any e>0 there exists a 5>0 such that for any X with -7r<X<7r and any element a in B which lies in the subspace L(K) = {a in B: ff(o)C [X -5, X + 8]} we have ||(V -e*)«a\\ ^ e\\a\\. Moreover the space B is spanned by a finite collection of such manifolds.
doi:10.1090/s0002-9939-67-99982-0 fatcat:wqkv2dyjrrasnhrzt6tk4iqssm