A combinatorial approach to monotonic independence over a C*-algebra
Operator Algebras
2008-09-05 v3 Functional Analysis
Abstract
The notion of monotonic independence, introduced by N. Muraki, is considered in a more general frame, similar to the construction of operator-valued free probability. The paper presents constructions for maps with similar properties to the H and K transforms from the literature, semi inner-product bimodule analogues for the monotone and weakly monotone product of Hilbert spaces, an ad-hoc version of the Central Limit Theorem, an operator-valued arsine distribution as well as a connection to operator-valued conditional freeness.
Cite
@article{arxiv.math/0612570,
title = {A combinatorial approach to monotonic independence over a C*-algebra},
author = {Mihai Popa},
journal= {arXiv preprint arXiv:math/0612570},
year = {2008}
}
Comments
final version, published in PJM