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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(mu$,H), for a $sigma$ - finite measure $mu$ and an arbitrary Hilbert space H, in terms of regular set isomorphisms of the $sigma$ - algebra involved and strongly measurable families of surjective isometries of H, is extended to arbitrary measures.
📌 3 Key Takeaways
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Objective & Hypothesis:In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(mu$,H), for a $sigma$ - finite measure $mu$ and an arbitrary Hilbert space H, in terms of regular set isomorphisms of the $sigma$ - algebra involved and strongly measurable families of surjective isometries of H, is extended to arbitrary measures.
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Key Findings & Data:In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(mu$,H), for a $sigma$ - finite measure $mu$ and an arbitrary Hilbert space H, in terms of regular set isomorphisms of the $sigma$ - algebra involved and strongly measurable families of surjective isometries of H, is extended to arbitrary measures.
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Conclusion & Impact:In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(mu$,H), for a $sigma$ - finite measure $mu$ and an arbitrary Hilbert space H, in terms of regular set isomorphisms of the $sigma$ - algebra involved and strongly measurable families of surjective isometries of H, is extended to arbitrary measures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this article, the known characterization of the surjective linear isometries of the Bochner space $L^p(mu$,H), for a $sigma$ - finite measure $mu$ and an arbitrary Hilbert space H, in terms of regular set isomorphisms of the $sigma$ - algebra involved and strongly measurable families of surjective isometries of H, is extended to arbitrary measures.
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Cite This Article
CENGİZ, B. (2022). The isometries of the Bochner space $L^p(mu$,H). Turkish Journal of Mathematics, Cilt: 23 - Sayı: 3, 389–399. https://ajindex.com/articles/608979