A combinatorial approach to monotonic independence over a C^∗-algebra

Mihai Popa

Vol. 237 (2008), No. 2, 299–325

DOI: 10.2140/pjm.2008.237.299

Abstract

We consider the notion of monotonic independence 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 arcsine distribution as well as a connection to operator-valued conditional freeness.

Keywords

monotonic independence, Hilbert bimodule

Mathematical Subject Classification 2000

Primary: 46L53

Secondary: 46L08

Milestones

Received: 1 March 2007

Revised: 27 March 2008

Accepted: 7 April 2008

Published: 1 October 2008