摘要
Theoperatorsets,whicharethesubjectofthispaper,havebeenstudiedinmanypaperswhere,underdifferentrestrictionsonthegeneratingoperators,convexity,compactnessintheweakoperatortopology,andnonemptinesswereprovedforsetsofdifferentclassesunderstudy.Thentheresultsobtainedwereusedinthesepaperstosolveseveralappliedproblems.Namely,theyplayedthekeyroleinestablishingthedichotomyofnonautonomousdynamicalsystems,witheithercontinuousordiscretetime.Inthepresentpaper,wegeneralizeandsharpenthealreadyknowncriteriaandobtainseveralnewcriteriaforconvexity,compactness,andnonemptinessofseveralspecialoperatorsets.Then,usingtheassertionsobtained,weconstructexamplesofsetsoftheformunderstudywhicharenonconvex,noncompactintheweakoperatortopology,aswellasempty,andaregeneratedby'smooth'operatorsofaspecialclass.Theexistenceproblemforsuchsetsremainedopenuntiltheauthorsofthispaperannouncedsomeofitsresults.
出版日期
2006年06月16日（中国期刊网平台首次上网日期，不代表论文的发表时间）
