Bounded and compact vectorial Hankel operators

Abstract

Operators H H satisfying S ∗ H = H S {S^ \ast }H = HS where S S is a unilateral shift on Hilbert space are called Hankel operators. For a fixed shift S S of arbitrary multiplicity the Banach spaces of bounded Hankel operators and of compact Hankel operators are described, and it is shown that the former is always the second dual of the latter. Representations for bounded and for compact Hankel operators are given in a standard function space model.