The Numerical Range of C*ψ Cφ and Cφ C*ψ
In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc. In the case when |a| = |b| = 1 we characterize the numerical range of these operators by constructing lacunary...
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De Gruyter
2021
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oai:doaj.org-article:a6f938265f49418380e8dd9339217f782021-12-05T14:10:45ZThe Numerical Range of C*ψ Cφ and Cφ C*ψ2299-328210.1515/conop-2020-0108https://doaj.org/article/a6f938265f49418380e8dd9339217f782021-03-01T00:00:00Zhttps://doi.org/10.1515/conop-2020-0108https://doaj.org/toc/2299-3282In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc. In the case when |a| = |b| = 1 we characterize the numerical range of these operators by constructing lacunary polynomials of unit norm whose image under the quadratic form incrementally foliate the numerical range. In the case when a and b are small we show numerical range of both operators is equal to the numerical range of the operator restricted to a 3-dimensional subspace.Clifford JohnDabkowski MichaelWiggins AlanDe Gruyterarticlecomposition operatornumerical rangeinner functionweighted shift47b3347a1215a60MathematicsQA1-939ENConcrete Operators, Vol 8, Iss 1, Pp 13-23 (2021) |
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composition operator numerical range inner function weighted shift 47b33 47a12 15a60 Mathematics QA1-939 |
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composition operator numerical range inner function weighted shift 47b33 47a12 15a60 Mathematics QA1-939 Clifford John Dabkowski Michael Wiggins Alan The Numerical Range of C*ψ Cφ and Cφ C*ψ |
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In this paper we investigate the numerical range of C*bφm Caφn and Caφn C*bφm on the Hardy space where φ is an inner function fixing the origin and a and b are points in the open unit disc. In the case when |a| = |b| = 1 we characterize the numerical range of these operators by constructing lacunary polynomials of unit norm whose image under the quadratic form incrementally foliate the numerical range. In the case when a and b are small we show numerical range of both operators is equal to the numerical range of the operator restricted to a 3-dimensional subspace. |
| format |
article |
| author |
Clifford John Dabkowski Michael Wiggins Alan |
| author_facet |
Clifford John Dabkowski Michael Wiggins Alan |
| author_sort |
Clifford John |
| title |
The Numerical Range of C*ψ Cφ and Cφ C*ψ |
| title_short |
The Numerical Range of C*ψ Cφ and Cφ C*ψ |
| title_full |
The Numerical Range of C*ψ Cφ and Cφ C*ψ |
| title_fullStr |
The Numerical Range of C*ψ Cφ and Cφ C*ψ |
| title_full_unstemmed |
The Numerical Range of C*ψ Cφ and Cφ C*ψ |
| title_sort |
numerical range of c*ψ cφ and cφ c*ψ |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/a6f938265f49418380e8dd9339217f78 |
| work_keys_str_mv |
AT cliffordjohn thenumericalrangeofcpscphandcphcps AT dabkowskimichael thenumericalrangeofcpscphandcphcps AT wigginsalan thenumericalrangeofcpscphandcphcps AT cliffordjohn numericalrangeofcpscphandcphcps AT dabkowskimichael numericalrangeofcpscphandcphcps AT wigginsalan numericalrangeofcpscphandcphcps |
| _version_ |
1718371768016568320 |