EXTENSIONS OF OPERATOR-VALUED MEASURES

Abstract

The extension of an operator-valued measure which is defined on an algebra and is countably additive with respect to the strong operator topology on a Hilbert space to the σ-algebra generated by the algebra is an important step in the construction of a spectral resolution for a normal operator ([1], [10]). This extension process was generalized to weaklysequentially complete Banach spaces by Kluvanek and Kovarikova and used to treat the product of spectral measures ([13]). In this note we observe that the Kluvanek-Kovarikova result can be extended to B-spaces which contain no copy of c0. We then indicate