On the continuity of the spectrum in certain Banach algebras

In this paper we describe some classes of linear operators T is an element of L(H) (mainly Toeplitz, Wiener-Hopf and singular integral) on a Hilbert s paces H such that the spectrum sigma (T,L(H)) is continuous at the points T from these classes. We also describe some subalgebras A of the algebras (A ) over tilde for which the spectrum sigma (x, (A) over tilde) becomes conti nuous at the points x when sigma (x, (A) over tilde) is restricted to the s ubalgebra A. In particular, we show that the spectrum sigma (x, (A) over ti lde) is continuous in Banach algebras (A) over tilde with polynomial identi ties. Examples of such algebras are given. (1)