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María Isabel Ramírez

Publications and source records attributed to María Isabel Ramírez.

3 recordsLinked to original sources
arXiv2017

The Mazur-Ulam property for the space of complex null sequences

Given an infinite set $Γ$, we prove that the space of complex null sequences $c_0(Γ)$ satisfies the Mazur-Ulam property, that is, for each Banach space $X$, every surjective isometry from the unit sphere of $c_0(Γ)$ onto the unit sphere of $X$ admits a (unique) extension to a surjective real linear isometry from $c_0(Γ)$ to $X$. We also prove that the same conclusion holds for the finite dimensional space $\ell_{\infty}^m$.

math.FA↗
arXiv2017

Pointwise-generalized-inverses of linear maps between C$^*$-algebras and JB$^*$-triples

We study pointwise-generalized-inverses of linear maps between C$^*$-algebras. Let $Φ$ and $Ψ$ be linear maps between complex Banach algebras $A$ and $B$. We say that $Ψ$ is a pointwise-generalized-inverse of $Φ$ if $Φ(aba)=Φ(a)Ψ(b)Φ(a),$ for every $a,b\in A$. The pair $(Φ,Ψ)$ is Jordan-triple multiplicative if $Φ$ is a pointwise-generalized-inverse of $Ψ$ and the latter is a pointwise-generalized-inverse of $Φ$. We study the basic properties of this maps in connection with Jordan homomorphism, triple homomorphisms and strongly preservers. We also determine conditions to guarantee the automatic continuity of the pointwise-generalized-inverse of continuous operator between C$^*$-algebras. An appropriate generalization is introduced in the setting of JB$^*$-triples.

math.OA↗
arXiv2014

Weak-local derivations and homomorphisms on C*-algebras

We prove that every weak-local derivation on a C$^*$-algebra is continuous, and the same conclusion remains valid for weak$^*$-local derivations on von Neumann algebras. We further show that weak-local derivations on C$^*$-algebras and weak$^*$-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal $^*$-automorphism with our notions of extreme-strong-local derivations and automorphisms.

math.OA↗