Inequalities for square functions induced by operators on a Hilbert space

Abstract

Let U:H→H be a unitary operator on a Hilbert space H and for all . Suppsoe that (nk) is a lacunary sequence with no non-trivial common divisor, then there exists a positive constant C such thatLet T be a contraction on a Hilbert space H and letfor all . Suppose that (nk) is a lacunary sequence with no non-trivial common divisor, then there exist a Hilbert space K containing H as a closed subspace, and an ortogonal projection P:K→H such that Mathematics Subject Classification: 47A63.