Dilations of Linear Maps on Vector Spaces
Functional Analysis
2021-04-16 v1 Operator Algebras
Abstract
We continue the study dilation of linear maps on vector spaces 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 can not be characterized.
Cite
@article{arxiv.2104.07544,
title = {Dilations of Linear Maps on Vector Spaces},
author = {K. Mahesh Krishna and P. Sam Johnson},
journal= {arXiv preprint arXiv:2104.07544},
year = {2021}
}
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11 pages