Operator-Valued Moment Series of the Generating Operator of L(F₂) Over the Commutator Group von Neumann algebra L(K)

2005/01/24 by Cho, Ilwoo
#47 xx #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0501368

Abstract

In this paper, we will consider the generating operator of the free group factor L(F₂). Then we can construct the group von Neumann algebra L(K), where K is the commutator group of F₂ and the conditional expectation E. Then (L(F₂), E) is the W*-probability space with amalgamation over L(K). In this paper, we will compute the trivial operator-valued moment series of the generating operator of L(F₂) over L(K). This computation is the good example for studying the operator-valued distribution, since the operator-valued moment series of operator-valued random variables contain algebraic and combinatorial free probability information about the opeartor-valued distributions.

Related

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• Moment Series and R-transform of the Generating Operator of L(F_N)
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• The Moments of the Block Operators in a Group von Neumann Algebra
• The Moment of an Operator in the Free Group Factor L(F_N)