Operator valued frames

Understand

We develop a natural generalization of vector-valued frame theory, we term operator-valued frame theory, using operator-algebraic methods.

• This extends work of the second author and D.
• Han which can be viewed as the multiplicity one case and extends to higher multiplicity (e.g., multiframes) their dilation approach.
• We prove several results for operator-valued frames concerning their parametrization, duality, disjointeness, complementarity, and composition and the relationship between the two types of similarity (left and right) of such frames.