相关论文: Surjective isometries between unitary sets of unit…

Let $M$ and $N$ be unital Jordan-Banach algebras, and let $M^{-1}$ and $N^{-1}$ denote the sets of invertible elements in $M$ and $N$, respectively. Suppose that $\mathfrak{M}\subseteq M^{-1}$ and $\mathfrak{N}\subseteq N^{-1}$ are clopen…

Let $M$ and $N$ be two unital JB$^*$-algebras and let $\mathcal{U} (M)$ and $\mathcal{U} (N)$ denote the sets of all unitaries in $M$ and $N$, respectively. We prove that the following statements are equivalent: $(a)$ $M$ and $N$ are…

We study maps between positive definite or positive semidefinite cones of unital $C^*$-algebras. We describe surjective maps that preserve (1) the norm of the quotient or multiplication of elements; (2) the spectrum of the quotient or…

In this note we collect some significant contributions on metric invariants for complex Banach algebras and Jordan--Banach algebras established during the last fifteen years. This note is mainly expository, but it also contains complete…

We prove that unital surjective spectral isometries on certain non-simple unital C*-algebras are Jordan isomorphisms. Along the way, we establish several general facts in the setting of semisimple Banach algebras.

We prove that for a bijective, unital, linear map between absolute order unit spaces is an isometry if, and only if, it is absolute value preserving. We deduce that, on (unital) $JB$-algebras, such maps are precisely Jordan isomorphisms.…

In this paper we describe all surjective isometries between open subgroups of the groups of invertible elements in unital $C^{*}$-algebras.

Let $M$ be a unital JB$^*$-algebra whose closed unit ball is denoted by $\mathcal{B}_M$. Let $\partial_e(\mathcal{B}_M)$ denote the set of all extreme points of $\mathcal{B}_M$. We prove that an element $u\in \partial_e(\mathcal{B}_M)$ is a…

We study surjective maps between the sets of all self-adjoint elements of unital $C^*$-algebras which satisfy the multiplicatively spectrum-preserving property. We show that such maps are characterized by Jordan isomorphisms and central…

Let $T: A\to B$ be a (not necessarily surjective) linear isometry between two real JB$^*$-triples. Then for each $a\in A$ there exists a tripotent $u_a$ in the bidual, $B'',$ of $B$ such that \begin{enumerate}[$(a)$] \item…

We investigate surjective isometries between projection lattices of two von Neumann algebras. We show that such a mapping is characterized by means of Jordan $^*$-isomorphisms. In particular, we prove that two von Neumann algebras without…

We prove that every JBW$^*$-triple $M$ with rank one or rank bigger than or equal to three satisfies the Mazur--Ulam property, that is, every surjective isometry from the unit sphere of $M$ onto the unit sphere of another Banach space $Y$…

Let $\mathfrak{M}$ and $\mathfrak{J}$ be JBW$^*$-algebras admitting no central summands of type $I_1$ and $I_2,$ and let $\Phi: \mathfrak{M} \rightarrow \mathfrak{J}$ be a linear bijection preserving operator commutativity in both…

Let $A$ and $B$ be C$^*$-algebras. A linear map $T:A\to B$ is said to be a $^*$-homomorphism at an element $z\in A$ if $a b^*=z$ in $A$ implies $T (a b^*) =T (a) T (b)^* =T(z)$, and $ c^* d=z$ in $A$ gives $T (c^* d) =T (c)^* T (d) =T(z).$…

We study holomorphic maps between C$^*$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_{A}(0,\delta)$ and we assume…

It is shown that every linear surjective isometry between two right, full, Hilbert C*-modules is a sum of two maps : a (bi-) module map (which is completely isometric and preserves the inner product) and a map that reverses the (bi-) module…

We show that any order isomorphism between ordered structures of associative unital JB-subalgebras of JBW algebras is implemented naturally by a Jordan isomorphism. Consequently, JBW algebras are determined by the structure of their…

Let $\mathfrak{A}$ and $\mathfrak{B}$ be JBW$^*$-algebras whose sets of unitaries are denoted by $\mathcal{U}(\mathfrak{A})$ and $\mathcal{U}(\mathfrak{B})$, respectively. We show that $\mathcal{U}(\mathfrak{A})$ is closed for Jordan…

For a C*-algebra A, G. Pedersen defined the concept of universal measurability for self-adjoint elements of A**, the universal enveloping algebra of A. Although he was unable to show that U, the set of universally measurable elements, is a…

It is shown that every linear strong Birkhoff-James isomorphism between unital $C^*$-algebras is a $*$-isomorphism followed by a unitary multiplication. Moreover, as a partial extension of this result to the non-unital case, the form of…