Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913868914098176 |
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| author | Kalenda, Ondřej F. K. Rondoš, Jakub Spurný, Jiří |
| author_facet | Kalenda, Ondřej F. K. Rondoš, Jakub Spurný, Jiří |
| contents | We develop a theory of abstract intermediate function spaces on a compact convex set $X$ and study the behaviour of multipliers and centers of these spaces. In particular, we provide some criteria for coincidence of the center with the space of multipliers and a general theorem on boundary integral representation of multipliers. We apply the general theory in several concrete cases, among others to strongly affine Baire functions, to the space $A_f(X)$ of fragmented affine functions, to the space $(A_f(X))^μ$, the monotone sequential closure of $A_f(X)$, to their natural subspaces formed by Borel functions, or, in some special cases, to the space of all strongly affine functions. In addition, we prove that the space $(A_f(X))^μ$ is determined by extreme points and provide a large number of illustrating examples and counterexamples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_16920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces Kalenda, Ondřej F. K. Rondoš, Jakub Spurný, Jiří Functional Analysis 46A55, 46J25, 54C30, 54C08, 54H05, 26A21 We develop a theory of abstract intermediate function spaces on a compact convex set $X$ and study the behaviour of multipliers and centers of these spaces. In particular, we provide some criteria for coincidence of the center with the space of multipliers and a general theorem on boundary integral representation of multipliers. We apply the general theory in several concrete cases, among others to strongly affine Baire functions, to the space $A_f(X)$ of fragmented affine functions, to the space $(A_f(X))^μ$, the monotone sequential closure of $A_f(X)$, to their natural subspaces formed by Borel functions, or, in some special cases, to the space of all strongly affine functions. In addition, we prove that the space $(A_f(X))^μ$ is determined by extreme points and provide a large number of illustrating examples and counterexamples. |
| title | Boundary integral representation of multipliers of fragmented affine functions and other intermediate function spaces |
| topic | Functional Analysis 46A55, 46J25, 54C30, 54C08, 54H05, 26A21 |
| url | https://arxiv.org/abs/2305.16920 |