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arXiv · 2604.20408

Ces\`aro-Hardy operators on $L^p[0,1]$: fine spectrum, weighted Koopman semigroups and invariant subspaces

Luciano Abadías·Alejandro Mahillo·Pedro J. Miana
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Abstract

In this paper we study boundedness and detailed spectral properties for the Ces\`aro-Hardy operator and some generalizations in $L^p[0,1]$. The study employs $C_0$-semigroup theory, expressing the Ces\`aro-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 Ces\`aro-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.

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Luciano Abadías, Alejandro Mahillo, Pedro J. Miana. 2026-04-22. Ces\`aro-Hardy operators on $L^p[0,1]$: fine spectrum, weighted Koopman semigroups and invariant subspaces. https://arxiv.org/abs/2604.20408

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