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The structure of linear zero product and commutativity preservers of C∗-algebras.
- Source :
- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM; Oct2021, Vol. 115 Issue 4, p1-12, 12p
- Publication Year :
- 2021
-
Abstract
- Let θ : A sa → B sa be a bijective real linear zero product preserver between the self-adjoint parts of two (complex) C ∗ -algebras. Suppose θ preserves commutativity in two directions (i.e., a b = b a if and only if θ (a) θ (b) = θ (b) θ (a) ). We show that θ is automatically continuous. More precisely, there is an invertible central self-adjoint multiplier h of B , and a real linear Jordan isomorphism J : A sa → B sa such that θ = h J . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 15787303
- Volume :
- 115
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales / RACSAM
- Publication Type :
- Periodical
- Accession number :
- 152505837
- Full Text :
- https://doi.org/10.1007/s13398-021-01134-z