Maps that preserve higher-dimensional numerical ranges with operator Jordan products

Chen, Chaoqun; Lu, Fangyan

doi:10.1080/03081087.2016.1278197

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Lemma 35 φ(I ) = ±I1

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Cited by 5 publications

(2 citation statements)

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“…Proof The case |η| = 1 and |η| = 0 were showed in [5] and in [6], respectively. In the following, we assume that |η| = 0, 1.…”

Section: Lemma 35 φ(I ) = ±Imentioning

confidence: 91%

Nonlinear maps preserving higher-dimensional numerical ranges of Jordan $$*$$-products

Chen

2019

Ann. Funct. Anal.

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Let H and K be complex Hilbert spaces. Denote by B(H ) and B(K ) the algebras of all bounded linear operators on H and K , respectively. In this paper, we characterize that nonlinear map φ : B(H ) → B(K ) that preserves the higher-dimensional numerical ranges of Jordan * -products. KeywordsHigher-dimensional numerical range • Nonlinear map • Jordan η- * -product Mathematics Subject Classification 47B49 • 46L10 B Chaoqun Chen

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“…Proof The case |η| = 1 and |η| = 0 were showed in [5] and in [6], respectively. In the following, we assume that |η| = 0, 1.…”

Section: Lemma 35 φ(I ) = ±Imentioning

confidence: 91%

Nonlinear maps preserving higher-dimensional numerical ranges of Jordan $$*$$-products

Chen

2019

Ann. Funct. Anal.

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“…Let H be a complex Hilbert space with inner product ·, · , B(H) and Obviously, if k = 1, we get the classical numerical range W (A) and the numerical radius w(A) of A. If (c 1 , ..., c k ) = (1, ..., 1), W c (A) and r c (A) reduce to k-numerical range and k-numerical radius of A, respectively ( [4,8,10]). Numerical range (radius) and c-numerical range (radius) are important concepts and have many applications in pure and applied mathematics, especially in quantum control and quantum information.…”

Section: Introductionmentioning

confidence: 99%

The c-numerical range of operator products on $${\mathcal {B}}(H)$$

Zhang

Fang

2019

Banach J. Math. Anal.

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Let H be a complex Hilbert space of dimension ≥ 2 and B(H) be the algebra of all bounded linear operators on H. We give the form of surjective maps on B(H) preserving c-numerical range of operator products when the maps satisfy preserving weak zero products. As a result, we obtain the characterization of surjective maps on M n (C) preserving c-numerical range of operator products. The proof of the results depends on some propositions of operators in B(H), which are of different interest.

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Higher Dimensional Numerical Range of $$\xi $$-Lie Products on Bound Self-adjoint Operators

Sun

Qi²

2023

Complex Anal. Oper. Theory

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Maps that preserve higher-dimensional numerical ranges with operator Jordan products

Cited by 5 publications

References 19 publications

Nonlinear maps preserving higher-dimensional numerical ranges of Jordan $$*$$-products

Nonlinear maps preserving higher-dimensional numerical ranges of Jordan $$*$$-products

The c-numerical range of operator products on $${\mathcal {B}}(H)$$

Higher Dimensional Numerical Range of $$\xi $$-Lie Products on Bound Self-adjoint Operators

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