Strongly continuous fields of operators over varying Hilbert spaces

2025/09/09 by Ali BenAmor, BenAmor, Ali, Batu Güneysu +5
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2509.07479

openalex publication_date 2025/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After introducing a natural notion of continuous fields of locally convex spaces, we establish a new theory of strongly continuous families of possibly unbounded self-adjoint operators over varying Hilbert spaces. This setting allows to treat operator families defined on bundles of Hilbert spaces that are not locally trivial (such as e.g.~the tangent bundle of Wasserstein space), without referring to identification operators at all.

Citations

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