Faculty Publications
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Publications by NITK Faculty
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Item 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.Item DILATION THEOREM FOR p-APPROXIMATE SCHAUDER FRAMES FOR SEPARABLE BANACH SPACES(Palestine Polytechnic University, 2022) Mahesh Krishna, K.M.; Johnson, P.S.Famous Naimark-Han-Larson dilation theorem for frames in Hilbert spaces states that every frame for a separable Hilbert space H is the image of a Riesz basis under an orthogonal projection from a separable Hilbert space H1 which contains H isometrically. In this paper, we derive dilation result for p-approximate Schauder frames for separable Banach spaces. Our result contains Naimark-Han-Larson dilation theorem as a particular case. © Palestine Polytechnic University-PPU 2022.Item Frames for Metric Spaces(Birkhauser, 2022) Mahesh Krishna, K.M.; Johnson, P.S.We make a systematic study of frames for metric spaces. We prove that every separable metric space admits a metric Md-frame. Through Lipschitz-free Banach spaces we show that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. We derive some characterizations of metric frames. We also derive stability results for metric frames. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.Item APPROXIMATELY DUAL p-APPROXIMATE SCHAUDER FRAMES(Austral Internet Publishing, 2023) Mahesh Krishna, K.M.; Johnson, P.S.Approximately dual frame in Hilbert spaces was introduced by Christensen and Laugesen to overcome difficulties in constructing dual frames for a given Hilbert space frame. It becomes even more difficult in Banach spaces to construct duals. For this purpose, we introduce approximately dual frames for a class of approximate Schauder frames for Banach spaces and develop basic theory. Approximate dual for this subclass is completely characterized and its perturbation is also studied. © 2023 Austral Internet Publishing. All rights reserved