# Dilations of linear maps on vector spaces

@article{Krishna2022DilationsOL, title={Dilations of linear maps on vector spaces}, author={K. Mahesh Krishna and P. S. Johnson}, journal={Operators and Matrices}, year={2022} }

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…

## 3 Citations

### Algebraic And\^{o} Dilation

- Mathematics
- 2022

: We solve the Andˆo dilation problem for linear maps on vector space asked by Krishna and Johnson in [Oper. Matrices, 2022] . More precisely, we show that any commuting linear maps on vector space…

### Indefinite Halmos, Egervary and Sz.-Nagy Dilations

- MathematicsSSRN Electronic Journal
- 2022

: Let M be an indeﬁnite inner product module over a *-ring of characteristic 2. We show that every self-adjoint operator on M admits Halmos, Egervary and Sz.-Nagy dilations.

### p-adic Magic Contractions, p-adic von Neumann Inequality and p-adic Sz.-Nagy Dilation

- MathematicsSSRN Electronic Journal
- 2022

: We introduce the notion of p-adic magic contraction on p-adic Hilbert space. We derive p-adic Halmos dilation, p-adic Egervary N-dilation, p-adic von Neumann inequality and p-adic Sz.-Nagy dilation…

## References

SHOWING 1-10 OF 35 REFERENCES

### A toolkit for constructing dilations on Banach spaces

- MathematicsProceedings of the London Mathematical Society
- 2018

We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if X is a super‐reflexive Banach space and T is…

### Structural Properties of Homomorphism Dilation Systems

- Mathematics
- 2020

Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach…

### Dilations of operator-valued measures with bounded p-variations and framings on Banach spaces

- Mathematics
- 2018

### Dilations of frames, operator valued measures and bounded linear maps

- Mathematics
- 2014

We will give an outline of the main results in our recent AMS Memoir, and include some new results, exposition and open problems. In that memoir we developed a general dilation theory for operator…

### Harmonic Analysis of Operators on Hilbert Space

- Mathematics
- 1970

Contractions and Their Dilations.- Geometrical and Spectral Properties of Dilations.- Functional Calculus.- Extended Functional Calculus.- Operator-Valued Analytic Functions.- Functional Models.-…

### A caricature of dilation theory

- MathematicsAdvances in Operator Theory
- 2021

We present a set-theoretic version of some basic dilation results of operator theory. The results we have considered are Wold decomposition, Halmos dilation, Sz. Nagy dilation, inter-twining lifting,…

### Framings and dilations

- MathematicsActa Scientiarum Mathematicarum
- 2013

The notion of framings, recently emerging in P. G. Casazza, D. Han, and D. R. Larson, Frames for Banach spaces, in {\em The functional and harmonic analysis of wavelets and frames} (San Antonio, TX,…

### ON UNITARY DILATIONS OF CONTRACTIONS

- Mathematics
- 2010

Using some relatively deep facts about complex functions and spectral measures, B. Sz.-Nagy [2] has recently proved that to every contraction A on a Hilbert space H there corresponds a unitary…

### Dilations of Positive Contractions on Lp Spaces*

- MathematicsCanadian Mathematical Bulletin
- 1977

Throughout this article p denotes a fixed number such that 1 ≤ p < ∞. The definition of a real Lp space associated with a measure space is well known. These spaces are Banach Spaces and, with the…

### Dilation Theory: A Guided Tour

- Mathematics
- 2020

Dilation theory is a paradigm for studying operators by way of exhibiting an operator as a compression of another operator which is in some sense well behaved. For example, every contraction can be…