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Displaying 3841 –
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A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.
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...
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....
We study a certain class of von Neumann algebras generated by selfadjoint elements , where satisfy the general commutation relations:
.
We assume that the operator T for which the constants 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...
In this paper we show that a Rosenthal operator factors through a Banach space containing no isomorphs of l1.
We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.
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