Isometries of JB-algebras |
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| Authors: | José M Isidro Angel Rodríguez Palacios |
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| Institution: | (1) Departmento de Análisis Matemático Facultad de Matemáticas, Universidad de Santiago, 15706 Santiago de Compostela, Spain;(2) Departmento de Análisis Matemático Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain |
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| Abstract: | A bijective linear mapping between two JB-algebrasA andB is an isometry if and only if it commutes with the Jordan triple products ofA andB. Other algebraic characterizations of isometries between JB-algebras are given. Derivations on a JB-algebraA are those bounded linear operators onA with zero numerical range. For JB-algebras of selfadjoint operators we have: IfH andK are left Hilbert spaces of dimension ≥3 over the same fieldF (the real, complex, or quaternion numbers), then every surjective real linear isometryf fromS(H) ontoS(K) is of the formf(x)=UoxoU
−1 forx inS(H), whereτ is a real-linear automorphism ofF andU is a real linear isometry fromH ontoK withU(λh)=τ(λ)U(h) for λ inF andh inH.
Supported by Acción Integrada Hispano-Alemana HA 94 066 B |
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