arXiv subjects

Georgios Katsimpas

Publications and source records attributed to Georgios Katsimpas.

3 recordsLinked to original sources

arXiv2021

Bi-Free Entropy with Respect to Completely Positive Maps

In this paper, a notion of non-microstate bi-free entropy with respect to completely positive maps is constructed thereby extending the notions of non-microstate bi-free entropy and free entropy with respect to a completely positive map. By extending the operator-valued bi-free structures to allow for more analytical arguments, a notion of conjugate variables is constructed using both moment and cumulant expressions. The notions of free Fisher information and entropy are then extended to this setting and used to show minima of the Fisher information and maxima of the non-microstate bi-free entropy at bi-R-diagonal elements.

math.OA↗

arXiv2019

Embedding $\mathrm{C}^*$-algebras into the Calkin algebra

Every $\mathrm{C}^*$-algebra, regardless of its density character, can be embedded into the Calkin algebra in a forcing extension of the universe obtained without collapsing any cardinal.

math.LO↗

arXiv2019

On Bi-R-Diagonal Pairs of Operators

We study the properties of the analogue of R-diagonal operators in the setting of bi-free probability. Products of bi-R-diagonal pairs of operators that are $*$-bi-free are studied and powers of such pairs are found to also be bi-R-diagonal. It is moreover shown that the joint $*$-distribution of a bi-R-diagonal pair of operators remains invariant under the multiplication by a $*$-bi-free bi-Haar unitary pair and equivalent characterizations of bi-R-diagonal pairs are developed.

math.OA↗