ABSTRACT
To keep similarity with [15], we denote this Hilbert space by H , and call it the Hilbert subspace of X** associated with R .
The proofs of [15, Propositions III.1.6 and III.1.7], which are stated for the case of a covariance operator R : X* X, work also in the case of R : X* X**. Thus, we state here those two propositions in the more general case of R : X* X**.
