English

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.

Keywords

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

R2 v1 2026-07-22T17:48:06.673Z