arXiv:2204.02516 · Linear Algebra and its Applications

Compositions and tensor products of linear maps between matrix algebras

Seung-Hyeok Kye

Published Nov 15, 2022• 6 citations

arXiv HTML PDF

DOI: 10.1016/j.laa.2022.11.002

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arXiv:2204.02516 · Linear Algebra and its Applications

Compositions and tensor products of linear maps between matrix algebras

Seung-Hyeok Kye

Published Nov 15, 2022• 6 citations

arXiv HTML PDF

DOI: 10.1016/j.laa.2022.11.002

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Erling Størmer

Using the natural duality between linear functionals on tensor products of $C^*$ -algebras with the trace class operators on a Hilbert space $H$ and linear maps of the $C^*$ -algebra into $B(H)$ , we give two characterizations of separability, one relating it to abelianness of the definite set of the map, and one on tensor products of nuclear and UHF $C^*$ -algebras.Using the natural duality between linear functionals on tensor products of $C^*$-algebras with the trace class operators on a Hilbert space $H$ and linear maps of the $C^*$-algebra into $B(H)$, we give two characterizations of separability, one relating it to abelianness of the definite set of the map, and one on tensor products of nuclear and UHF $C^*$-algebras.

MATHEMATICA SCANDINAVICADec 1, 200915 citations

Using the natural duality between linear functionals on tensor products of

C^*

-algebras with the trace class operators on a Hilbert space

H

and linear maps of the

C^*

-algebra into

B(H)

, we give two characterizations of separability, one relating it to abelianness of the definite set of the map, and one on tensor products of nuclear and UHF

C^*

-algebras.