Some remarks on abstract Universal series

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• 作者：I.  ; Kyrezi^a ;   ; ^{ioanna.kyrezi@gmail.com} ; V.  ; Nestoridis^b ;   ; ^{vnestor@math.uoa.gr} ; C.  ; Papachristodoulos^c ;   ; ^{papach@math.uoc.gr}
• 关键词：Universal series ; Abstract theory of Universal series ; Baire?s Category Theorem ; Generic property ; Taylor series ; Upper density ; Lower density
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：15 March 2012
• 年：2012
• 卷：387
• 期：2
• 页码：878-884
• 全文大小：154 K

文摘

We introduce a new class of Universal series, in the abstract setting. This class lies between two already known classes of Universal series. By two examples we differentiate these classes. These examples are the first examples in the case where all classes are non-void. We also prove that the class of Universal series where the approximating indexes have upper density 1 is dense and and that the class of lower frequently universal series is of the first category.