Journal of the Ramanujan Mathematical Society

Volume 38, Issue 4, December 2023 pp. 369–392.

Operator-valued p-approximate Schauder frames

Authors: K. Mahesh Krishna and P. Sam Johnson
Author institution: Statistics and Mathematics Unit, Indian Statistical Institute, Bangalore Centre, Bengaluru, Karnataka 560 059, India.

Summary: We give an operator-algebraic treatment of the theory of p-approximate Schuader frames which includes the theory of operator-valued frames studied by Kaftal, Larson, and Zhang [Trans. AMS., 2009], G-frames studied by Sun [J. Math. Anal. Appl., 2006], factorable weak operator-valued frames studied by Krishna and Johnson [Ann. Funct. Anal., 2022] and p-approximate Schauder frames studied by Krishna and Johnson [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.

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