Faculty Publications

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Towards characterizations of approximate Schauder frame and its duals for Banach spaces
(Birkhauser, 2021) Mahesh Krishna, K.M.; Johnson, P.S.
Characterizations for a frame and its duals are known for separable Hilbert spaces. In this paper, we characterize a class of approximate Schauder frame and its duals for separable Banach spaces. We also give an operator-theoretic characterization for similarity of ASFs. Our results encode the results of Holub, Li, Balan, Han, and Larson. We also address orthogonality of ASFs. © 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature.
Expansion of weak reconstruction sequences to approximate Schauder frames for Banach spaces
(World Scientific, 2022) Mahesh Krishna, K.M.; Johnson, P.S.
It is known in Hilbert space frame theory that a Bessel sequence can be expanded to a frame. Contrary to Hilbert space situation, using a result of Casazza and Christensen, we show that there are Banach spaces and weak reconstruction sequences which cannot be expanded to approximate Schauder frames. We characterize Banach spaces in which one can expand weak reconstruction sequences to approximate Schauder frames. © 2022 World Scientific Publishing Company.