Two-Variable Compressions of Shifts, Toeplitz Operators, and Numerical Ranges
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917325324681216 |
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| author | Bickel, Kelly Quertermous, Katie Trachana, Matina |
| author_facet | Bickel, Kelly Quertermous, Katie Trachana, Matina |
| contents | This paper studies two-variable compressions of shifts associated to rational inner functions on the bidisk; these generalize the classical compressions of the shift associated to finite Blasckhe products and are unitarily equivalent to one-variable, matrix-valued Toeplitz operators. This paper proves that a rational inner function is almost completely determined by these Toeplitz operator symbols but provides examples showing that (unlike in the one-variable case) rational inner functions are not determined by the numerical ranges of their compressed shifts. This paper also investigates related questions including methods of constructing these compressed-shift Toeplitz operators and when the associated numerical ranges are open and closed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08559 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Two-Variable Compressions of Shifts, Toeplitz Operators, and Numerical Ranges Bickel, Kelly Quertermous, Katie Trachana, Matina Complex Variables Functional Analysis Primary 47B32, 47A13, Secondary 47A12, 47B35, 32A08 This paper studies two-variable compressions of shifts associated to rational inner functions on the bidisk; these generalize the classical compressions of the shift associated to finite Blasckhe products and are unitarily equivalent to one-variable, matrix-valued Toeplitz operators. This paper proves that a rational inner function is almost completely determined by these Toeplitz operator symbols but provides examples showing that (unlike in the one-variable case) rational inner functions are not determined by the numerical ranges of their compressed shifts. This paper also investigates related questions including methods of constructing these compressed-shift Toeplitz operators and when the associated numerical ranges are open and closed. |
| title | Two-Variable Compressions of Shifts, Toeplitz Operators, and Numerical Ranges |
| topic | Complex Variables Functional Analysis Primary 47B32, 47A13, Secondary 47A12, 47B35, 32A08 |
| url | https://arxiv.org/abs/2603.08559 |