$H^\infty$ Functional Calculus for a Commuting Pair of $\text{Ritt}_{\text{E}}$ Operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910150569230336 |
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| author | Mondal, Suman Palai, Subhajit Ray, Samya Kumar |
| author_facet | Mondal, Suman Palai, Subhajit Ray, Samya Kumar |
| contents | In this article, we develop a framework for the joint functional calculus of commuting pair of $\text{Ritt}_{\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus for pair of $\text{Ritt}_{\text{E}}$ operators to that of their associated sectorial counterparts. In addition, we prove a joint dilation theorem for commuting tuples of $\text{Ritt}_{\text{E}}$ operators on a broad class of Banach spaces. As a key application, we obtain an equivalent set of criteria on $L^p$-spaces for $1<p< \infty$ that determine when a commuting pair of $\text{Ritt}_{\text{E}}$ operators admits a joint bounded functional calculus. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_05788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $H^\infty$ Functional Calculus for a Commuting Pair of $\text{Ritt}_{\text{E}}$ Operators Mondal, Suman Palai, Subhajit Ray, Samya Kumar Functional Analysis In this article, we develop a framework for the joint functional calculus of commuting pair of $\text{Ritt}_{\text{E}}$ operators on Banach spaces. We establish a transfer principle that relates the bounded holomorphic functional calculus for pair of $\text{Ritt}_{\text{E}}$ operators to that of their associated sectorial counterparts. In addition, we prove a joint dilation theorem for commuting tuples of $\text{Ritt}_{\text{E}}$ operators on a broad class of Banach spaces. As a key application, we obtain an equivalent set of criteria on $L^p$-spaces for $1<p< \infty$ that determine when a commuting pair of $\text{Ritt}_{\text{E}}$ operators admits a joint bounded functional calculus. |
| title | $H^\infty$ Functional Calculus for a Commuting Pair of $\text{Ritt}_{\text{E}}$ Operators |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.05788 |