On matrix-valued frames over measure spaces

Let [Formula: see text] be a measure space, where [Formula: see text] is [Formula: see text]-finite and [Formula: see text] is countably generated. We study matrix-valued frames in the matrix-valued function space [Formula: see text]. First, we give frame conditions for a family of functions in the space [Formula: see text] in terms of frames for its atomic spaces. Contrary to what happens with matrix-valued Bessel sequences in [Formula: see text], it is not true that the lower frame condition for [Formula: see text] can be carried to its associated atomic space [Formula: see text]. We give the construction of matrix-valued frames from strongly disjoint Bessel sequences associated with atomic functions. A necessary and sufficient condition for the existence of matrix-valued tight frames is given. Matrix-valued dual frame pairs of the space [Formula: see text] are presented. Numerical examples are given to support our results.