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pro vyhledávání: '"Garcés, Jorge"'
Let $\{C_i\}_{i\in \Gamma_1},$ and $\{D_j\}_{j\in \Gamma_2},$ be two families of Cartan factors such that all of them have dimension at least $2$, and consider the atomic JBW$^*$-triples $A=\bigoplus\limits_{i\in \Gamma_1}^{\ell_{\infty}} C_i$ and $B
Externí odkaz:
http://arxiv.org/abs/2405.13489
Autor:
Garcés, Jorge J., Khrypchenko, Mykola
Let $X$ be an arbitrary poset and $K$ an arbitrary field. We describe linear unital invertibility preservers of the finitary incidence algebra $FI(X,K)$ in terms of certain maps of the power set algebra $\mathcal{P}(X)$ and linear maps $FI(X,K)\to J(
Externí odkaz:
http://arxiv.org/abs/2404.08393
Publikováno v:
J.Math. Anal. Appl 376 (1), 221-230 (2011)
We prove that every biorthogonality preserving linear surjection between two dual or compact C$^*$-algebras or between two von Neumann algebras is automatically continuous.
Comment: arXiv admin note: text overlap with arXiv:2402.00517
Comment: arXiv admin note: text overlap with arXiv:2402.00517
Externí odkaz:
http://arxiv.org/abs/2402.00914
Autor:
Garcés, Jorge J., Peralta, Antonio M.
Publikováno v:
Canad. J. Math. 65 (2013), 783-807
We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by Jarosz and Johnson in 1985 and 1987, respectively. We prove that ever
Externí odkaz:
http://arxiv.org/abs/2402.00682
Publikováno v:
Proceedings of the American Mathematical Society 140 (9), 3179-3191 (2012)
Let $T:E\rightarrow F$ be a non-necessarily continuous triple homomorphism from a (complex) JB$^*$-triple (respectively, a (real) J$^*$B-triple) to a normed Jordan triple. The following statements hold: (1) $T$ has closed range whenever $T$ is contin
Externí odkaz:
http://arxiv.org/abs/2402.00538
Publikováno v:
Studia Math 204 (2), 97-121 (2011)
We prove that every biorthogonality preserving linear surjection from a weakly compact JB$^*$triple containing no infinite dimensional rank-one summands onto another JB$^*$-triple is automatically continuous. We also show that every biorthogonality p
Externí odkaz:
http://arxiv.org/abs/2402.00517
Autor:
Garcés, Jorge J.
Publikováno v:
Journal of Mathematical Analysis and Applications 483 (1), 123596 (2020)
We introduce $n$-orthogonality (and completely orthogonality) preserving operators between C$^*$-algebras. Our main theorem states that every completely orthogonality preserving bounded linear mapping between C$^*$-algebras is a weighted TRO homomorp
Externí odkaz:
http://arxiv.org/abs/2402.00503
Autor:
Garcés, Jorge J., Khrypchenko, Mykola
We study bounded bilinear maps on a C$^*$-algebra $A$ having product property at $c\in A$. This leads us to the question of when a C$^*$-algebra is determined by products at $c.$ In the first part of our paper, we investigate this question for compac
Externí odkaz:
http://arxiv.org/abs/2310.06595
We introduce the Jordan-strict topology on the multipliers algebra of a JB$^*$-algebra, a notion which was missing despite the fourty years passed after the first studies on Jordan multipliers. In case that a C$^*$-algebra $A$ is regarded as a JB$^*$
Externí odkaz:
http://arxiv.org/abs/2210.13353
Autor:
Garcés, Jorge J., Khrypchenko, Mykola
Let $A$, $B$ be algebras and $a\in A$, $b\in B$ a fixed pair of elements. We say that a map $\varphi:A\to B$ preserves products equal to $a$ and $b$ if for all $a_1,a_2\in A$ the equality $a_1a_2=a$ implies $\varphi(a_1)\varphi(a_2)=b$. In this paper
Externí odkaz:
http://arxiv.org/abs/2206.01788