A note on the boundary of the joint numerical range

Chan, Jor-Ting

doi:10.1080/03081087.2017.1326455

Cited by 6 publications

(2 citation statements)

References 11 publications

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“…Its proof is based on an idea of Williams from . For a different, geometrical proof of the statement see (and also [, Theorem 2.1 and Corollary 2.3] for related results). Theorem Let

T = false(T_{1}, \dots, T_{n} false) \in B {(H)}^{n}

.…”

Section: Joint Numerical Ranges Revisitedmentioning

confidence: 99%

Joint numerical ranges and compressions of powers of operators

Müller

Tomilov

2018

J. London Math. Soc.

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We identify subsets of the joint numerical range of an operator tuple in terms of its joint spectrum. This result helps us to transfer weak convergence of operator orbits into certain approximation and interpolation properties for powers in the uniform operator topology. This is a far‐reaching generalization of one of the main results in our recent paper [Müller and Tomilov, J. Funct. Anal. 274 (2018) 433–460]. Moreover, it yields an essential (but partial) generalization of Bourin's ‘pinching’ theorem from [Bourin, J. Operator Theory 50 (2003) 211–220]. It also allows us to revisit several basic results on joint numerical ranges, provide them with new proofs and find a number of new results.

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“…Its proof is based on an idea of Williams from . For a different, geometrical proof of the statement see (and also [, Theorem 2.1 and Corollary 2.3] for related results). Theorem Let

T = false(T_{1}, \dots, T_{n} false) \in B {(H)}^{n}

.…”

Section: Joint Numerical Ranges Revisitedmentioning

confidence: 99%

Joint numerical ranges and compressions of powers of operators

Müller

Tomilov

2018

J. London Math. Soc.

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“…There have been a number of generalizations of this result, including by Chan [3] and Chan, Li and Poon [4]. Chan [3] generalized this to the joint numerical range of an n-tuple of operators, whereas Chan, Li and Poon [4] generalized it to the k-numerical range.…”

Section: Introductionmentioning

confidence: 99%

Closedness of the orbit-closed $C$-numerical range and submajorization

Loreaux¹,

Patnaik²

2021

Preprint

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For a positive trace-class operator C and a bounded operator A, we provide an explicit description of the closure of the orbit-closed C-numerical range of A in terms of those operators submajorized by C and the essential numerical range of A. This generalizes and subsumes recent work of Chan, Li and Poon for the k-numerical range, as well as some of our own previous work on the orbit-closed C-numerical range.

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