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aequationes mathematicae

, Volume 55, Issue 3, pp 259–272 | Cite as

Characterization of additive *-homomorphisms and Jordan *-homomorphisms on operator ideals

  • L. Molnár
  • 34 Downloads

Abstract.

Let H be a separable complex Hilbert space and let \( \cal {B (H)} \) denote the algebra of all bounded linear operators on H. It is proved that if \( \cal {I} \subset \cal {B (H)} \) is an ideal, then the additive function \( \Phi : \cal {I} \to \cal {B (H)} \) is a Jordan *-homomorphism if and only if it satisfies¶¶$ \Phi (A^*A + AA^*) = \Phi (A)^* \Phi (A) + \Phi (A) \Phi(A)^* \qquad (A \in \cal {I}). $¶Similarly, \( \Phi \) is a *-homomorphism if and only if it satisfies¶¶$ \Phi (A^*A) = \Phi (A)^* \Phi (A) \qquad (A \in \cal {I}). $¶These functional equations come from noncommutative approximation theory.

Keywords. Jordan *-homomorphism, Jordan-Schwarz map, operator ideal. 

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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • L. Molnár
    • 1
  1. 1.Institute of Mathematics, Lajos Kossuth University, P. O. Box 12, H-4010 Debrecen, Hungary, e-mail: molnarl@math.klte.huHU

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