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arXiv · 1503.03353

Relative nuclearity for $\mathrm{C}^*$-algebras and $KK$-equivalences of amalgamated free products

Kei Hasegawa
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Abstract

We prove a relative analogue of equivalence between nuclearity and CPAP. In its proof, the notion of weak containment for C$^*$-correspondences plays an important role. As an application we prove $KK$-equivalence between full and reduced amalgamated free products of C$^*$-algebras under a strengthened variant of `relative nuclearity'.

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Kei Hasegawa. 2015-03-11. Relative nuclearity for $\mathrm{C}^*$-algebras and $KK$-equivalences of amalgamated free products. https://arxiv.org/abs/1503.03353

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