Functional decompositions on vector-valued function spaces via operators

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• 作者：Titarii Wootijirattikal^a ; ^b ; ¹ ; ^{sctitawo@ubu.ac.th} ; ^{ma_pintto@yahoo.com} ; Sing-Cheong Ong^c ; ² ; ^{ong1s@cmich.edu} ; ^{ong3pf@gmail.com} ; Jitti Rakbud^d ; ^{jitti@su.ac.th} ; ^{jitrakbud@yahoo.com}
• 关键词：Banach space ; C?/sup>-algebra ; State space ; Weak?/sup> topology
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：15 May 2012
• 年：2012
• 卷：389
• 期：2
• 页码：1173-1190
• 全文大小：278 K

文摘

Let X be a Banach space with a generalized basis. The Banach algebra of bounded linear operators on X is used to construct Banach spaces, and , of weak^{?/sup> continuous functions from the state space of a -algebra to . If the basis satisfies certain properties, we prove that the dual space of has a decomposition analogous to that of the dual space of . In terms of the notion of M-ideal introduced by Alfsen and Effros, the subspace is an M-ideal in the Banach space . For the cases of and , , we also prove an analogue of the result that for a trace class operator A and a bounded operator B on a Hilbert space.}