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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.
DILATIONS OF LINEAR MAPS ON VECTOR SPACES
(Element D.O.O., 2022) Mahesh Krishna, K.M.; Johnson, P.S.
Dilation of linear maps on vector spaces has been recently introduced by Bhat, De, and Rakshit. This notion is a variant of vector space dilation introduced by Han, Larson, Liu, and Liu. We derive vector space versions of Wold decomposition, Halmos dilation, N-dilation, inter-twining lifting theorem and a variant of Ando dilation. It is noted further that unlike a kind of uniqueness of Halmos dilation of strict contractions on Hilbert spaces, vector space version of Halmos dilation cannot be characterized. © 2022, Element D.O.O.. All rights reserved.