Remarks on the bidual of Banach algebras (the case)
Bruno Iochum, Guy Loupias (1991)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Bruno Iochum, Guy Loupias (1991)
Annales scientifiques de l'Université de Clermont. Mathématiques
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Takeshi Miura (2011)
Open Mathematics
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Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A → B is a surjective real-linear isometry, then there exist a continuous function κ: ChB → z ∈ ℂ: |z| = 1, a (possibly empty) closed and open subset K of ChB and a homeomorphism φ: ChB → ChA such that T(f) = κ(f ∘φ) on K and on ChB K for all f ∈ A. Such a representation holds for surjective real-linear isometries between (not...
Ferdinand Beckhoff (1993)
Mathematica Slovaca
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Antonio Fernández López, Eulalia García Rus (1986)
Extracta Mathematicae
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Dina Štěrbová (1983)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Tewari, U.B., Dutta, M., Madan, Shobha (1982)
International Journal of Mathematics and Mathematical Sciences
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Rachid ElHarti, Mohamed Mabrouk (2015)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Let A and B be two non-unital reduced Banach *-algebras and φ: A → B be a vector space isomorphism. The two following statement holds: If φ is a *-isomorphism, then φ is isometric (with respect to the C*-norms), bipositive and φ maps some approximate identity of A onto an approximate identity of B. Conversely, any two of the later three properties imply that φ is a *-isomorphism. Finally, we show that a unital and self-adjoint spectral isometry between semi-simple Hermitian Banach algebras...