Cesàro-Hardy operators on $L^p[0,1]$: fine spectrum, weighted Koopman semigroups and invariant subspaces
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| Format: | Preprint |
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2026
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| _version_ | 1866913057648672768 |
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| author | Abadías, Luciano Mahillo, Alejandro Miana, Pedro J. |
| author_facet | Abadías, Luciano Mahillo, Alejandro Miana, Pedro J. |
| contents | In this paper we study boundedness and detailed spectral properties for the Cesàro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Cesàro-Hardy operators and their dual operators through subordination with $C_0$-semigroups $T(t)$ and $S(t)$ respectively. The spectral properties of the semigroup's infinitesimal generators are transferred to the Cesàro-Hardy operators using functional calculus methods. Furthermore, some implications for the Invariant Subspace Problem are explored by demonstrating the universality of certain translations related to the semigroup $T(t)$, and providing results on the invariant subspaces of these operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_20408 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cesàro-Hardy operators on $L^p[0,1]$: fine spectrum, weighted Koopman semigroups and invariant subspaces Abadías, Luciano Mahillo, Alejandro Miana, Pedro J. Functional Analysis Spectral Theory 47A10, 47A15, 47B33, 47D03, 47G10 In this paper we study boundedness and detailed spectral properties for the Cesàro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Cesàro-Hardy operators and their dual operators through subordination with $C_0$-semigroups $T(t)$ and $S(t)$ respectively. The spectral properties of the semigroup's infinitesimal generators are transferred to the Cesàro-Hardy operators using functional calculus methods. Furthermore, some implications for the Invariant Subspace Problem are explored by demonstrating the universality of certain translations related to the semigroup $T(t)$, and providing results on the invariant subspaces of these operators. |
| title | Cesàro-Hardy operators on $L^p[0,1]$: fine spectrum, weighted Koopman semigroups and invariant subspaces |
| topic | Functional Analysis Spectral Theory 47A10, 47A15, 47B33, 47D03, 47G10 |
| url | https://arxiv.org/abs/2604.20408 |