A functional representation approach to vector lattice covers for spaces of compact operators
Year: 2025
Type: preprint
Abstract: For ordered normed vector spaces $X, Y$, we consider the space $\mathcal{L}(X,Y)$ of bounded linear operators and characterize when its cone of positive operators has non-empty interior. When this is satisfied, we give a functional representation of the closure $\mathcal{C}(X,Y)$ of the finite rank operators in $\mathcal{L}(X,Y)$. This space is particularly interesting since it coincides in many cases with the space of compact operators from $X$ to $Y$. Our functional representation has very good order properties in the sense that it is a so-called vector lattice cover of $\mathcal{C}(X,Y)$. This can be used to characterize disjointness of operators in $\mathcal{C}(X,Y)$ and to determine which operators have a modulus in $\mathcal{C}(X,Y)$. We demonstrate how our results can be applied to a variety of concrete spaces.
Source: arXiv (Cornell University)
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979229787
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