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Facial structures of separable and PPT states

Seung-Hyeok Kye (2011)

Banach Center Publications

A positive semi-definite block matrix (a state if it is normalized) is said to be separable if it is the sum of simple tensors of positive semi-definite matrices. A state is said to be entangled if it is not separable. It is very difficult to detect the border between separable and entangled states. The PPT (positive partial transpose) criterion tells us that the partial transpose of a separable state is again positive semi-definite, as was observed by M. D. Choi in 1982 from...

Factor representations of diffeomorphism groups

Robert P. Boyer (2003)

Studia Mathematica

We give a new construction of semifinite factor representations of the diffeomorphism group of euclidean space. These representations are in canonical correspondence with the finite factor representations of the inductive limit unitary group. Hence, many of these representations are given in terms of quasi-free representations of the canonical commutation and anti-commutation relations. To establish this correspondence requires a generalization of complete positivity as developed in operator algebras....

Factoriality of von Neumann algebras connected with general commutation relations-finite dimensional case

Ilona Królak (2006)

Banach Center Publications

We study a certain class of von Neumann algebras generated by selfadjoint elements ω i = a i + a i , where a i , a i satisfy the general commutation relations: a i a j = r , s t j i r s a r a s + δ i j I d . We assume that the operator T for which the constants t j i r s are matrix coefficients satisfies the braid relation. Such algebras were investigated in [BSp] and [K] where the positivity of the Fock representation and factoriality in the case of infinite dimensional underlying space were shown. In this paper we prove that under certain conditions on the number of generators...

Factoring Rosenthal operators.

Teresa Alvarez (1988)

Publicacions Matemàtiques

In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l1.

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