arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1008.3733math.OAmath.FA
收藏

C*-子代数的Leibniz半范数与最佳逼近

Leibniz Seminorms and Best Approximation from C*-subalgebras

Marc A. Rieffel

备注：
24 pages. Intended for the proceedings of the conference "Operator Algebras and Related Topics". v2: added a corollary to the main theorem, plus several minor improvements v3: much simplified proof of a key lemma, corollary to main theorem added v4: Many minor improvements. Section numbers increased by 1
发表信息：
Sci China Math, 2011, 54(11): 2259-2274
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

证明了：如果B是C* 代数A的C*-子代数，使得B包含A的有界逼近恒等式，且L是A/B上的商范数向A的拉回，则L是强Leibniz.针对这种情况，我们研究了有单位元的C* 代数的元用有单位元的C * 子代数的元的最佳逼近的某些方面.

英文摘要：

We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑