The space of ideals in the minimal tensor product of $C^*$-algebras

Aldo J. Lazar

doi:10.1017/S0305004109990351

paper

The space of ideals in the minimal tensor product of $C^{*}$ -algebras

arXiv:0904.3216 · doi:10.1017/S0305004109990351

Abstract

For $C^{*}$ -algebras $A_{1}, A_{2}$ the map $(I_{1}, I_{2}) \to k er (q_{I_{1}} \otimes q_{I_{2}})$ from $I d^{'} (A_{1}) \times I d^{'} (A_{2})$ into $I d^{'} (A_{1} \otimes_{min} A_{2}) i s ah o m eo m or p hi s m o n t o i t s ima g e w hi c hi s d e n se in t h er an g e . H er e, f or a$ C^* $- a l g e b r a$ A $, t h es p a ceo f a l l p r o p er c l ose d tw os i d e d i d e a l se n d o w e d w i t hana d e q u a t e t o p o l o g y i s d e n o t e d$ Id^{\prime}(A) $an d$ q_I $i s t h e q u o t i e n t ma p o f$ A $o n t o$ A/I $. N e w p r oo f so f t h ee q u i v a l e n ceo f t h e p r o p er t y (F) o f T o mi y ama f or$ A_1\otimes_{\mathrm{min}} A_2$ with certain other properties are presented.

9 pages, minor mistakes were corrected

Cited by in corpus (1)

On Banach space projective tensor product of $C^{*}$ -algebras

The space of ideals in the minimal tensor product of C∗-algebras

Abstract

Cited by in corpus (1)

The space of ideals in the minimal tensor product of $C^{*}$ -algebras