scholarly journals Dilation theory in finite dimensions and matrix convexity

2021 ◽  
Author(s):  
Michael Hartz ◽  
Martino Lupini
Keyword(s):  
Dilation Theory ◽  
Matrix Convexity

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

Dilation Theory

2016 ◽  
pp. 137-162
Author(s):  
Paul Busch ◽  
Pekka Lahti ◽  
Juha-Pekka Pellonpää ◽  
Kari Ylinen
Keyword(s):  
Dilation Theory
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