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Duality and operator algebras: automatic weak▫$^\ast$▫ continuity and applications
Blecher, David P., 1962- ; Magajna, Bojan
Za vsak podprostor ▫$C^\ast$▫-algebre ▫$A$▫ in tak element ▫$a \in A$▫, da je ▫$aX \subseteq X$▫ pokažemo, da je preslikava ▫$x \mapsto ax$▫ avtomatično šibko▫$^\ast$▫ zvezna, če je izpolnjen eden od ...pogojev: (1) ▫$X$▫ je dualni operatorski prostor ali pa (2) ▫$a^\ast X \subseteq X$▫ in ▫$X$▫ je dualni Banachov prostor. Za dokaz najprej posplošimo na Banachove module znani Tomiyamin rezultat o projektorjihz normo 1 na ▫$C^\ast$▫-algebrah. Kot uporabo, dobimo novo karakterizacijo ne-sebiadjungiranih šibko▫$^\ast$▫ zaprtih operatorskih algeber in razširitev nekaterih aspektov teorije ▫$W^\ast$▫-modulov na module nad takimi algebrami. Karakteriziramo tudi Banachove module, ki dopuščajo strukturo dualnega operatorskega modula nad von Neumannovo algebro.
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