Wick Product for Commutation Relations Connected with Yang–Baxter Operators and New Constructions of Factors
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We analyze a certain class of von Neumann algebras generated by selfadjoint elements \(\), for \(\) satisfying the general commutation relations:
Such algebras can be continuously embedded into some closure of the set of finite linear combinations of vectors \(\), where \(\) is an orthonormal basis of a Hilbert space \(\). The operator which represents the vector \(\) is denoted by \(\) and called the “Wick product” of the operators \(\). We describe explicitly the form of this product. Also, we estimate the operator norm of \(\) for \(\). Finally we apply these two results and prove that under the assumption \(\) all the von Neumann algebras considered are II 1 factors.
KeywordsHilbert Space Linear Combination Operator Norm Orthonormal Basis Commutation Relation
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