Hardy operators: In the footsteps of Brown, Halmos, and Shields
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913664814022656 |
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| author | Gallardo-Guttierrez, Eva A. Partington, Jonathan R. Ross, William T. |
| author_facet | Gallardo-Guttierrez, Eva A. Partington, Jonathan R. Ross, William T. |
| contents | This paper discusses the two classical Hardy operators $\mathcal{H}_{1}$ on $L^2(0, 1)$ and $\mathcal{H}_{\infty}$ on $L^2(0, \infty)$ initially studied by Brown, Halmos and Shields. Particular emphasis is given to the construction of explicit cyclic and $*$-cyclic vectors in conjunction with a characterization of their invariant and reducing subspaces. We also provide a complete description of the frame vectors for $I - \mathcal{H}_{1}^{*}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14706 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hardy operators: In the footsteps of Brown, Halmos, and Shields Gallardo-Guttierrez, Eva A. Partington, Jonathan R. Ross, William T. Functional Analysis Complex Variables 47A15, 47A16, 47B15, 30H10 This paper discusses the two classical Hardy operators $\mathcal{H}_{1}$ on $L^2(0, 1)$ and $\mathcal{H}_{\infty}$ on $L^2(0, \infty)$ initially studied by Brown, Halmos and Shields. Particular emphasis is given to the construction of explicit cyclic and $*$-cyclic vectors in conjunction with a characterization of their invariant and reducing subspaces. We also provide a complete description of the frame vectors for $I - \mathcal{H}_{1}^{*}$. |
| title | Hardy operators: In the footsteps of Brown, Halmos, and Shields |
| topic | Functional Analysis Complex Variables 47A15, 47A16, 47B15, 30H10 |
| url | https://arxiv.org/abs/2501.14706 |