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On joint numerical ranges and joint normaloids in a C*-algebra

On joint numerical ranges and joint normaloids in a C*-algebra
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Joint k-numerical ranges of operators

Acta Scientiarum Mathematicarum, 2022
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Chan, Jor-Ting, Li, Chi-Kwong, Poon, Yiu-Tung   +2 more
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The joint numerical range of commuting matrices

Studia Mathematica, 2022
Let \(M_n\) be the space of \(n\times n\) complex matrices. The joint numerical range of an \(m\)-tuple of \(n\times n\) matrices \(\mathbf{A} = (A_1, \dots, A_m)\in M_n^m\) is defined as \[ W({\mathbf A}) =\{(x^*A_1x, \dots, x^*A_mx): x\in {\mathbb C}^n, x^*x=1\}, \] which is reduced to the classical numerical range of \(A_1\in M_n\) when \(m=1 ...
Lau, Pan-Shun, Li, Chi-Kwong, Poon, Yiu-Tung   +2 more
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Reduction of joint c-numerical ranges

Applied Mathematics and Computation, 2014
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Chien, M. T., Nakazato, H.
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Convexity of the Joint Numerical Range

SIAM Journal on Matrix Analysis and Applications, 2000
Let \(A=(A_1,\ldots,A_m)\) be an \(m\)-tuple of \(n\times n\) Hermitian matrices. For \(1\leq k\leq n,\) the \(k\)th joint numerical range of \(A\) is defined as \[ W_k(A)=\{(\text{tr}(X^\star A_1X),\dots,\text{tr}(X^\star A_mX))\mid X\in{\mathbb{C}}^{n\times k},X^\star X=I_k\}. \] The authors pose a number of problems, e.g.
Li, Chi-Kwong, Poon, Yiu-Tung
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Joint numerical range with degenerate boundary generating variety

Advances in Operator Theory, 2023
Let \(H_d\) be the real Hilbert space of Hermitian \(d\times d\) matrices with bilinear form \(\langle A,B\rangle=\textrm{tr}\,AB\), and let \[ \mathcal{B}_d=\{\rho\in H_d: \rho\text{ is nonnegative definite }\mathrm{tr}\,\rho=1\}. \] The joint (algebraic) numerical range of \((A_1,\dots,A_n)\in H_d^n\) is defined by \[ W(A_1,\dots,A_n)=\{(\langle A_1,\
Mao-Ting Chien, Hiroshi Nakazato
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Generalized joint higher-rank numerical range

2015
Summary: The rank-$k$ numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. For a noisy quantum channel, a quantum error correcting code of dimension $k$ exists, if and only if the associated joint rank-$k$ numerical range is non-empty.
Mehrjoofard, M. A., Afshin, H. R., Bagheri, S.   +2 more
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The joint essential maximal numerical range

Applied Mathematics and Computation, 2004
The author studies elementary properties of the joint essential numerical range, defined for an \(n\)-tuple \(T=(T_1,\ldots,T_n)\) of Hilbert space (linear and bounded) operators by the formula \[ \begin{multlined}\text{JtMax}V(T)=\{(f(t_1),\ldots,f(T_n)): f\in {\mathcal B}(H)^\ast, \;f(I)=1=\| f\|, \\ {}\qquad \text{and} \;f(T_j^\ast T_j)=\| T_j ...
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Pauli group: Classification and joint higher rank numerical range

Linear Algebra and its Applications, 2018
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Afshin, Hamid Reza, Mehrjoofard, Mohammad Ali, Chavoshi, Akbar Zare   +2 more
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