Characterizations of domains of fractional powers for non-negative operators

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• 作者：Chuang Chen ; ^{ccmath@scu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Miao Li ^{mli@scu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Non-negative operators ; Fractional powers ; Komatsu spaces ; Fractional resolvent families ; Functional calculi
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：435
• 期：1
• 页码：179-209
• 全文大小：538 K

文摘

It is known that a closed linear operator A, defined densely on a Banach space X, is non-negative if and only if −A generates a bounded analytic γ  -times resolvent family for some 0<γ<2$0<\gamma <2$. In this paper, by using such resolvent families as well as the Komatsu representations, we characterize systematically the domains of fractional powers of non-negative operators on Banach spaces. Gaps between the subset ⋃_α>0D(A^α)${\bigcup }_{\alpha >0}D(A^{\alpha })$ and the whole space X are discussed as well.