The structure and asymptotic behavior of polynomially compact operators
Frank L. Gilfeather · Proceedings of the American Mathematical Society · 1970
A. R. Bernstein and A. Robinson proved that every polynomially compact operator in Hilbert space has nontrivial invariant subspaces. This paper gives a structure theorem for these operators. We show that a polynomially compact operator is the finite sum of translates of operators which have the property that a finite power of the operator is compact. Furthermore, the spectrum of polynomially compact operators is completely described. Conditions are given to determine the weak and strong asymptotic behavior of a polynomially compact contraction in Hilbert space.