Banach Spaces with respect to Operator-Valued Norms

2008/03/01 by Yun-Su Kim, Kim, Yun-Su
Mathematics · #46B45 #46C07 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.FA #math.OA #msc:46B45 #msc:46C07

paper · pdf · doi:10.48550/arxiv.0803.0041

13 page

arxiv created 2008/03/01 · openalex publication_date 2008/03/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notions of L(H)-valued norms and Banach spaces with respect to L(H)-valued norms. In particular, we introduce Hilbert spaces with respect to L(H)-valued inner products. In addition, we provide several fundamental examples of Hilbert spaces with respect to L(H)-valued inner products.

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