Vol. 237, No. 2, 2008

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A combinatorial approach to monotonic independence over a Cāˆ—-algebra

Mihai Popa

Vol. 237 (2008), No. 2, 299ā€“325

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.

monotonic independence, Hilbert bimodule
Mathematical Subject Classification 2000
Primary: 46L53
Secondary: 46L08
Received: 1 March 2007
Revised: 27 March 2008
Accepted: 7 April 2008
Published: 1 October 2008
Mihai Popa
Indiana University at Bloomington
Department of Mathematics
Rawles Hall 309
831 E Third St
Bloomington, IN 47405
United States