Characterizations of Lie-skew multiplicative maps on operator algebras of indefinite inner product spaces

• Autores: Runling An, Jinchuan Hou
• Localización: Publicationes Mathematicae Debrecen, ISSN 0033-3883, Tomus 77, Fasc. 1-2, 2010, págs. 101-113
• Idioma: inglés
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• Resumen

  • Let H and K be inde¯nite inner product spaces. In this paper, we show that a bijective map © : B(H) ! B(K) satis¯es ©(AB ¡ BAy) = ©(A)©(B) ¡ ©(B)©(A)y for every pair A;B 2 B(H) if and only if there exist a unitary or conjugate unitary operator U 2 B(H;K) such that ©(A) = UAU y for all A 2 B(H).