DILATIONS OF LINEAR MAPS ON VECTOR SPACES

Authors

K. Mahesh Krishna, Indian Statistical Institute Bangalore
P. Sam Johnson, National Institute of Technology Karnataka

Article Type

Research Article

Publication Title

Operators and Matrices

Abstract

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.

First Page

465

Last Page

477

DOI

10.7153/oam-2022-16-36

Publication Date

6-1-2022

Comments

Open Access, Bronze, Green

Recommended Citation

Krishna, K. Mahesh and Johnson, P. Sam, "DILATIONS OF LINEAR MAPS ON VECTOR SPACES" (2022). Journal Articles. 3078.
https://digitalcommons.isical.ac.in/journal-articles/3078