Operator-valued integral of vector-function and bases - Faroughi, M. H. (Methods of Functional Analysis and Topology, 2007)
In the present paper we are going to introduce an operator-valued integral of a square modulus weakly integrable mappings the ranges of which are Hilbert spaces, as bounded operators. Then, we shall show that each operator-valued integrable mapping of the index set of an orthonormal basis of a Hilbert space H into H can be written as a multiple of a sum of three orthonormal bases.