Openness and weak openness of multiplication in the space of functions of bounded variation

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• 作者：Stanisław Kowalczyk ; ^{skowalczyk@apsl.edu.pl} ; Małgorzata Turowska ^{malgorzata.turowska@apsl.edu.pl}
• 关键词：Open mapping ; Weakly open mapping ; Space of continuous functions of bounded variation ; Multiplication in function spaces
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1560-1571
• 全文大小：346 K
• 卷排序：448

文摘

Let BV[0,1]BV[0,1] and CBV[0,1]CBV[0,1] be spaces of functions of bounded variation and continuous functions of bounded variation, respectively, with the norm ‖f‖BV=|f(0)|+V01(f). We shall show that the multiplication is a weakly open operation in BV[0,1]BV[0,1] and CBV[0,1]CBV[0,1]. Moreover, the multiplication is an open operation in BV[0,1]BV[0,1] with the standard supremum norm. Some other properties of multiplication in function spaces are studied.