Positive Operator Frame for Hilbert C*-modules

Abstract

The work on frame theory has undergone a remarkable evolution over the last century. Several related properties have applications on many fields of mathematics, engineering, signal and image processing, informatics, medecine and probability. In order to search for new results related to the role of operators in frame theory using the characterization of the positive elements in a C^∗-algebra, we introduce the concept of positive operator frame, L-positive operator frame, ∗-positive operator frame and ∗-L-positive operator frame for the set of all adjointable operators on a Hilbert C^∗-module denoted End^∗_B(H) where L is a positive operator. Also, we give some new properties.