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We characterize surjective nonlinear maps Φ between unital C*-algebras 𝒜 and ℬ that satisfy w(Φ(A)-Φ(B))) = w(A-B) for all A,B ∈ 𝒜 under a mild condition that Φ(I) - Φ(0) belongs to the center of ℬ, where w(A) is the numerical radius of A and I is the unit of 𝒜.
Zhaofang Bai, Jinchuan Hou, and Zongben Xu. "Maps preserving numerical radius distance on C*-algebras." Studia Mathematica 162.2 (2004): 97-104. <http://eudml.org/doc/284950>.
@article{ZhaofangBai2004, abstract = {We characterize surjective nonlinear maps Φ between unital C*-algebras 𝒜 and ℬ that satisfy w(Φ(A)-Φ(B))) = w(A-B) for all A,B ∈ 𝒜 under a mild condition that Φ(I) - Φ(0) belongs to the center of ℬ, where w(A) is the numerical radius of A and I is the unit of 𝒜.}, author = {Zhaofang Bai, Jinchuan Hou, Zongben Xu}, journal = {Studia Mathematica}, keywords = {numerical radius distance; -algebra; central projection; unitary element}, language = {eng}, number = {2}, pages = {97-104}, title = {Maps preserving numerical radius distance on C*-algebras}, url = {http://eudml.org/doc/284950}, volume = {162}, year = {2004}, }
TY - JOUR AU - Zhaofang Bai AU - Jinchuan Hou AU - Zongben Xu TI - Maps preserving numerical radius distance on C*-algebras JO - Studia Mathematica PY - 2004 VL - 162 IS - 2 SP - 97 EP - 104 AB - We characterize surjective nonlinear maps Φ between unital C*-algebras 𝒜 and ℬ that satisfy w(Φ(A)-Φ(B))) = w(A-B) for all A,B ∈ 𝒜 under a mild condition that Φ(I) - Φ(0) belongs to the center of ℬ, where w(A) is the numerical radius of A and I is the unit of 𝒜. LA - eng KW - numerical radius distance; -algebra; central projection; unitary element UR - http://eudml.org/doc/284950 ER -