Linear Maps Preserving Numerical Radius on Nest Algebras |
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Authors: | Fangyan Lu |
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Institution: | 1.Department of Mathematics,Soochow University,Suzhou,People’s Republic of China |
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Abstract: | A linear map \({\phi}\) of operator algebras is said to preserve numerical radius (or to be a numerical radius isometry) if \({w(\phi(A))=w(A)}\) for all A in its domain algebra, where w(A) stands for the numerical radius of A. In this paper, we prove that a surjective linear map \({\phi}\) of the nest algebra \({{\rm Alg}\mathcal N}\) onto itself preserves numerical radius if and only if there exist a unitary U and a complex number ξ of modulus one such that \({\phi(A)= \xi UAU^*}\) for all \({A\in{\rm Alg}\mathcal N}\), or there exist a unitary U, a conjugation J and a complex number ξ of modulus one such that \({\phi(A)=\xi UJA^*JU^*}\) for all \({A\in{\rm Alg}\mathcal N}\). |
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