$K$-Continuity Is Equivalent To $K$-Exactness

• Autores: Otgonbayar Uuye
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 118, Nº 1, 2016, págs. 95-105
• Idioma: inglés
• DOI: 10.7146/math.scand.a-23299
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• Resumen

  • Let $A$ be a $C^{*}$-algebra. It is well known that the functor $B \mapsto A \otimes B$ of taking the minimal tensor product with $A$ preserves inductive limits if and only if it is exact. $C^{*}$-algebras with this property play an important role in the structure and finite-dimensional approximation theory of $C^{*}$-algebras. We consider a $K$-theoretic analogue of this result and show that the functor $B \mapsto K_{0}(A \otimes B)$ preserves inductive limits if and only if it is half-exact.