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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...

Factorizing multilinear operators on Banach spaces, C*-algebras and JB*-triples

Carlos Palazuelos, Antonio M. Peralta, Ignacio Villanueva (2009)

Studia Mathematica

In recent papers, the Right and the Strong* topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong*-to-norm continuity of a multilinear operator T defined on C*-algebras (respectively, JB*-triples) to C*-summability (respectively, JB*-triple-summability)....

Finite generation in C*-algebras and Hilbert C*-modules

David P. Blecher, Tomasz Kania (2014)

Studia Mathematica

We characterize C*-algebras and C*-modules such that every maximal right ideal (resp. right submodule) is algebraically finitely generated. In particular, C*-algebras satisfy the Dales-Żelazko conjecture.

Finite sums and products of commutators in inductive limit C * -algebras

Klaus Thomsen (1993)

Annales de l'institut Fourier

Results of T. Fack, P. de la Harpe and G. Skandalis concerning the internal structure of simple A F -algebras are extended to C * -algebras that are inductive limits of finite direct sums of homogeneous C * -algebras. The generalizations are obtained with slightly varying assumptions on the building blocks, but all results are applicable to unital simple inductive limits of finite direct sums of circle algebras.

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