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Wu [‘An order characterization of commutativity for $C^{\ast }$-algebras’, Proc. Amer. Math. Soc.129 (2001), 983–987] proved that if the exponential function on the set of all positive elements of a $C^{\ast }$-algebra is monotone in the usual partial order, then the algebra in question is necessarily commutative. In this note, we present a local version of that result and obtain a characterisation of central elements in $C^{\ast }$-algebras in terms of the order. [ABSTRACT FROM PUBLISHER]

We prove that a bijective linear transformation between von Neumann factors that commute with a λ-Aluthge transform is necessarily a non-zero scalar multiple of an algebra *-isomorphism in the case of algebras that are not of type I2. As for type I2 factors, that is, in the particular case of the algebra of 2 by 2 complex matrices, we also present a complete description of those transformations which is a bit different. Namely, non-zero scalar multiples of the sum of an algebra *-antiisomorphism and the negative of the trace functional times the identity also show up. [ABSTRACT FROM AUTHOR]

In this paper, we determine the structure of certain algebraic morphisms and isometries of the spaceof allcomplex positive definite matrices. In the case, we describe all continuous Jordan triple endomorphisms ofwhich are continuous mapssatisfyingIt has recently been discovered that surjective isometries of certain substructures of groups equipped with metrics which are in a way compatible with the group operations have algebraic properties that relate them rather closely to Jordan triple morphisms. This makes us possible to use our structural results to describe all surjective isometries ofthat correspond to any member of a large class of metrics generalizing the geodesic distance in the natural Riemannian structure on. Finally, we determine the isometry group ofrelative to a very recently introduced metric that originates from the divergence called Stein’s loss. [ABSTRACT FROM AUTHOR]

We present a few characterizations of the commutativity of C*-algebras in terms of particular algebraic properties of power functions, the logarithmic and exponential functions, and the sine and cosine functions. [ABSTRACT FROM AUTHOR]