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- Title
CHARACTERIZATIONS OF JORDAN †-SKEW MULTIPLICATIVE MAPS ON OPERATOR ALGEBRAS OF INDEFINITE INNER PRODUCT SPACES.
- Authors
An Runling; Hou Jinchuan
- Abstract
Let H and K be indefinite inner product spaces. This paper shows that a bijective map Φ : B(H) → B(K) satisfies Φ(AB† + B† A) = Φ(A)Φ(B)† + Φ(B)†Φ(A) for every pair A,B ∊ B(H) if and only if either Φ(A) = cU AU† for all A or Φ(A) = cU A† U† for all A; Φ satisfies Φ(AB† A) = Φ(A)Φ(B)†Φ(A) for every pair A,B ∊ B(H) if and only if either Φ(A) = U AV for all A or Φ(A) = U A†V for all A, where A† denotes the indefinite conjugate of A, U and V are bounded invertible linear or conjugate linear operators with U†U = c-1 I and V†V = cI for some nonzero real number c.
- Subjects
INDEFINITE inner product spaces; OPERATOR algebras; JORDAN matrix; DIVISION rings; MATHEMATICAL mappings; CONJUGACY classes; LINEAR operators
- Publication
Chinese Annals of Mathematics, 2005, Vol 26, Issue 4, p569
- ISSN
0252-9599
- Publication type
Article
- DOI
10.1142/S0252959905000464