The algebraic numerical range as a spectral set in Banach algebras
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913696622575616 |
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| author | Blazhko, Hanna Homza, Daniil Schwenninger, Felix L. de Vries, Jens Wojtylak, Michał |
| author_facet | Blazhko, Hanna Homza, Daniil Schwenninger, Felix L. de Vries, Jens Wojtylak, Michał |
| contents | We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and provide an absolute constant in the case of complex $2\times2$-matrices with the induced $1$-norm. Furthermore, we discuss positive results for infinite-dimensional Banach algebras, including the Calkin algebra. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_10678 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The algebraic numerical range as a spectral set in Banach algebras Blazhko, Hanna Homza, Daniil Schwenninger, Felix L. de Vries, Jens Wojtylak, Michał Functional Analysis Numerical Analysis 47A25, 47A12, 47B48, 15A60 We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and provide an absolute constant in the case of complex $2\times2$-matrices with the induced $1$-norm. Furthermore, we discuss positive results for infinite-dimensional Banach algebras, including the Calkin algebra. |
| title | The algebraic numerical range as a spectral set in Banach algebras |
| topic | Functional Analysis Numerical Analysis 47A25, 47A12, 47B48, 15A60 |
| url | https://arxiv.org/abs/2410.10678 |