Extensions of an AC(σ) functional calculus

详细信息    查看全文

• 作者：Ian Doust ; Venta Terauds
• 关键词：Functional calculus ; Well-bounded operators ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4XCYJJT-2&_mathId=mml4&_user=10&_cdi=6894&_pii=S0022247X0900821X&_rdoc=11&_issn=0022247X&_a
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2010
• 出版时间：1 February 2010
• 年：2010
• 卷：362
• 期：1
• 页码：100-106
• 全文大小：185 K

文摘

On a reflexive Banach space X, if an operator T admits a functional calculus for the absolutely continuous functions on its spectrum , then this functional calculus can always be extended to include all the functions of bounded variation. This need no longer be true on nonreflexive spaces. In this paper, it is shown that on most classical separable nonreflexive spaces, one can construct an example where such an extension is impossible. Sufficient conditions are also given which ensure that an extension of an AC functional calculus is possible for operators acting on families of interpolation spaces such as the L^p spaces.