Operator-Valued p-Approximate Schauder Frames

Abstract: We give an operator-algebraic treatment of theory of p-approximate Schuader frames which includes the theory of operator-valued frames by Kaftal, Larson, and Zhang [\textit{Trans. AMS., 2009}], G-frames by Sun [JMAA, 2006], factorable weak operator-valued frames by Krishna and Johnson [\textit{Annals of FA, 2022}] and p-approximate Schauder frames by Krishna and Johnson [\textit{J. Pseudo-Differ. Oper. Appl, 2021}] as particular cases. We show that a sufficiently rich theory can be developed even for Banach spaces. We achieve this by defining various concepts and characterizations in Banach spaces. These include duality, approximate duality, equivalence, orthogonality and stability.