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arXiv · 2509.07479

Strongly continuous fields of operators over varying Hilbert spaces

Ali BenAmor·Batu Güneysu·Thomas Kalmes·Peter Stollmann
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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.

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Ali BenAmor, Batu Güneysu, Thomas Kalmes, Peter Stollmann. 2025-09-09. Strongly continuous fields of operators over varying Hilbert spaces. https://arxiv.org/abs/2509.07479

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