Foguel-type operators similar to contractions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917179935424512 |
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| author | Das, Nilanjan Das, Soma Sarkar, Jaydeb |
| author_facet | Das, Nilanjan Das, Soma Sarkar, Jaydeb |
| contents | Pisier's celebrated counterexample to Halmos's similarity-to-contractions problem was based on $2 \times 2$ upper triangular block operator matrices involving three classical operators: forward and backward shifts on the diagonal and Hankel operators in the off-diagonal entry. Together with another classical object, namely Toeplitz operators, one can formulate another $2^3 -1 = 7$ types of $2 \times 2$ upper triangular block operator matrices, which we refer to as Foguel-type operators. In this paper, we give a complete characterization of all the seven Foguel-type operators being similar to contractions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_00319 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Foguel-type operators similar to contractions Das, Nilanjan Das, Soma Sarkar, Jaydeb Functional Analysis Complex Variables Operator Algebras 47B35, 32A37, 15B05, 47B38, 46E40, 30H10, 30H35 Pisier's celebrated counterexample to Halmos's similarity-to-contractions problem was based on $2 \times 2$ upper triangular block operator matrices involving three classical operators: forward and backward shifts on the diagonal and Hankel operators in the off-diagonal entry. Together with another classical object, namely Toeplitz operators, one can formulate another $2^3 -1 = 7$ types of $2 \times 2$ upper triangular block operator matrices, which we refer to as Foguel-type operators. In this paper, we give a complete characterization of all the seven Foguel-type operators being similar to contractions. |
| title | Foguel-type operators similar to contractions |
| topic | Functional Analysis Complex Variables Operator Algebras 47B35, 32A37, 15B05, 47B38, 46E40, 30H10, 30H35 |
| url | https://arxiv.org/abs/2601.00319 |