On norm-preserving isomorphisms of $L^{p}(mu,H)$

Authors : Ba GÜNTÜRK, B CENGİZ, M GÜRDAL

Pages : 33-41

View : 51 | Download : 12

Publication Date : 2016-02-01

Article Type : Research Paper

Abstract :Given an arbitrary positive measure space $insert ignore into journalissuearticles values(X,A,\mu);$ and a Hilbert space $H$. In this article we give a new proof for the characterization theorem of the surjective linear isometries of the space $L^{p}insert ignore into journalissuearticles values(\mu,H);$ insert ignore into journalissuearticles values(for $1\leq p<\infty$, $p\neq 2$); which is essentially different from the existing one, and depends on the p-projections of $L^{p}insert ignore into journalissuearticles values(\mu,H);$. We generalize the known characterization of the p-projections of  $L^{p}insert ignore into journalissuearticles values(\mu,H);$ for $\sigma$-finite measure to the arbitrary case. They are proved to be the multiplication operations by the characteristic functions of the locally measurable sets, or that of the clopen insert ignore into journalissuearticles values(closed-open); subsets of the hyperstonean space the measure $\mu$ determines.
Keywords : Measure space, Bochner space, perfect measure, hyperstonean space, linear isometries

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