$C^*$-algebras with weak$^*$ angelic dual balls
$C^*$-algebras with weak$^*$ angelic dual balls
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$C^*$-具有弱$^*$天使双球的代数
DOI：
10.1090/bproc/50
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发表时间：
2020
期刊：
影响因子：
--
通讯作者：
Tanaka Ryotaro
中科院分区：
文献类型：
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作者：
Sain Debmalya;Tanaka Ryotaro;Tanaka Ryotaro
给出了具有弱角对偶球的弱Rickart-代数的遗传子代数的一些刻画。特别地，证明了对偶球的弱角性、弱序性和弱序紧性在这类代数上是相同的，并且利用这些代数中紧元素的理想来刻画它们。作为应用，证明了弱Rickart-代数有弱角对偶球当且仅当它与紧元理想重合，当且仅当该代数是有限维的。参考文献
Some characterizations of hereditary-subalgebras of weakly Rickart-algebras with weakangelic dual balls are given. In particular, it turns out that weakangelicity, weaksequentiality and weaksequential compactness of dual balls are the same on this class, and that they are characterized by using ideals of compact elements in those algebras. As an application, it is shown that a weakly Rickart-algebra has weakangelic dual ball if and only if it coincides with the ideal of compact elements, which happens if and only if the algebra is finite dimensional. References