تقرير
Homomorphic conditional expectations as noncommutative retractions
| العنوان: | Homomorphic conditional expectations as noncommutative retractions |
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| المؤلفون: | Pluta, Robert, Russo, Bernard |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, 46L99, 17C65 |
| الوصف: | Let $A$ be a $C^*$-algebra and $E\colon A \to A$ a conditional expectation. The Kadison-Schwarz inequality for completely positive maps, $$E(x)^*E(x) \leq E(x^* x),$$ implies that $$ \|E(x)\|^2 \leq \|E(x^* x)\|.$$ In this note we show that $E$ is a homomorphism if and only if $$\|E(x)\|^2 = \|E(x^*x)\|,$$ for every $x$ in $A$. We also prove that a homomorphic conditional expectation on a commutative $C^*$-algebra $C_0(X)$ is given by composition with a continuous retraction of $X$. One may therefore consider homomorphic conditional expectations as noncommutative retractions. Comment: Accepted by Advances in Operator Theory, 14 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1706.02442 |
| رقم الأكسشن: | edsarx.1706.02442 |
| قاعدة البيانات: | arXiv |
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