Local triple derivations on real C*-algebras and JB*-triples

We study when a local triple derivation on a real JB*-triple is a triple derivation. We find an example of a (real linear) local triple derivation on a rank-one Cartan factor of type I which is not a triple derivation. On the other hand, we find sufficient conditions on a real JB*-triple E to guarantee that every local triple derivation on E is a triple derivation

2-local triple homomorphisms on von Neumann algebras and JBW∗^*-triples

We prove that every (not necessarily linear nor continuous) 2-local triple homomorphism from a JBW$^*$-triple into a JB$^*$-triple is linear and a triple homomorphism. Consequently, every 2-local triple homomorphism from a von Neumann algebra (respectively, from a JBW$^*$-algebra) into a C$^*$-algebra (respectively, into a JB$^*$-algebra) is linear and a triple homomorphism

Local triple derivations on C*-algebras

We prove that every bounded local triple derivation on a unital C*-algebra is a triple derivation. A similar statement is established in the category of unital JB*-algebras.Comment: 12 pages, submitte

Tingley's problem for p-Schatten von Neumann classes

[EN] Let H and H' be the complex Hilbert spaces. For p is an element of] 1, infinity[\{2} we consider the Banach space C-p(H) of all p-Schatten von Neumann operators, whose unit sphere is denoted by S(C-p(H)). In this paper we prove that every surjective isometry Delta: S(C-p(H)) -> S(C-p(H')) can be extended to a complex linear or to a conjugate linear surjective isometry T: C-p(H) -> C-p(H').The first and third authors were partially supported by the Spanish Ministry of Science, Innovation and Universities (MICINN) and European RegionalDevelopment Fund project no. PGC2018-093332-B-I00, Programa Operativo FEDER 2014-2020 and Consejeria de Economia y Conocimiento de la Junta de Andalucia grant number A-FQM-242-UGR18, and Junta de Andalucia grant FQM375. The second author was partially supported by the project MTM2016-76647-P.Fernández-Polo, FJ.; Jorda Mora, E.; Peralta, AM. (2020). Tingley's problem for p-Schatten von Neumann classes. Journal of Spectral Theory. 10(3):809-841. https://doi.org/10.4171/JST/313S80984110

Magnetic transition in nanocrystalline soft magnetic alloys analyzed via ac inductive techniques

The magnetic transition in a FeSiBCuNb nanocrystalline alloy, associated with the decoupling of ferromagnetic crystallites around the Curie point of the residual amorphous matrix, is analyzed in this work through the temperature dependence of the ac axial magnetic permeability and impedance of the samples. The temperature dependence of both complex magnitudes presents a maximum in the irreversible contribution at a certain transition temperature. While for low values of the exciting ac magnetic field the transition temperature lies below the Curie temperature of the amorphous phase, a shift above this Curie point is observed increasing the amplitude of the applied ac magnetic field. The detected field dependence is interpreted taking into account the ac nature of the inductive characterization techniques and the actual temperature dependence of the coercivity of the samples

On the strict topology of the multipliers of a JB∗-algebra

Universidad de Granada/CBUA. F. J. Fernandez-Polo, J. J. Garces and A. M. Peralta partially supported by grant PID2021-122126NB-C31 funded by MCIN/AEI/10.13039/501100011033 and by "ERDF A way of making Europe", Junta de Andalucia grants FQM375 and PY20_00255,and by the IMAG-Mariade Maeztu grant CEX2020-001105-M/AEI/10.13039/501100011033.L. Li partially supported by NSF of China (12171251).We introduce the Jordan-strict topology on the multiplier algebra of a JB*-algebra, a notion which was missing despite the forty years passed after the first studies on Jordan multipliers. In case that a C*-algebra A is regarded as a JB*-algebra, the J-strict topology of M(A) is precisely the well-studied C*-strict topology. We prove that every JB*-algebra U is J-strict dense in its multiplier algebra M(U), and that latter algebra is J-strict complete. We show that continuous surjective Jordan homomorphisms, triple homomorphisms, and orthogonality preserving operators between JB*-algebras admit J-strict continuous extensions to the corresponding type of operators between the multiplier algebras. We characterize J-strict continuous functionals on the multiplier algebra of a JB*-algebra U, and we establish that the dual of M(U) with respect to the J-strict topology is isometrically isomorphic to U*. We also present a first application of the J-strict topology of the multiplier algebra, by showing that under the extra hypothesis that U and B are sigma-unital JB*-algebras, every surjective Jordan *-homomorphism (respectively, triple homomorphism or continuous orthogonality preserving operator) from U onto B admits an extension to a surjective J-strict continuous Jordan *-homomorphism (respectively, triple homomorphism or continuous orthogonality preserving operator) from M(U) onto M(B).Universidad de Granada/CBUAMCIN/AEI/ PID2021-122126NB-C31"ERDF A way of making Europe"Junta de Andalucia FQM375, PY20_00255MAG-Mariade Maeztu CEX2020-001105-M/AEI/10.13039/501100011033National Natural Science Foundation of China (NSFC) 1217125

Environmental and anthropogenic driven transitions in the demersal ecosystem of Cantabrian Sea

In the framework of global human-induced change, marine communities’ often respond to changing conditions abruptly reorganizing into new equilibria. These shifts are difficult to predict and often imply irreversible adjustments due to hysteresis. Unraveling the role of the forces leading regime shifts is a major challenge. We explored the temporal evolution of 63 fish species representing the Cantabrian bentho-demersal community in response to environmental changes and fishing pressure in the period 1983–2018, using survey data. Via multivariate analysis and non-additive modeling of a community index and the system's main stressors, two decadal-scale regimes were revealed, suggesting a non-linear response of the community to its environment. The Integrated Resilience Assessment framework elucidated the response mechanism to the candidate stressors and allowed quantifying resilience dynamics. The decline in fishing pressure in the 1990s was associated with a gradual transition of the system, while further decline during the 2000s eroded the resilience of the system towards changes in its stressors, leading to a discontinuous response expressed as an abrupt, possibly irreversible shift in the 2010s. Given the teleconnected character of marine ecosystems, this regional study endorses the scientific effort for actions facing the dynamic impacts of climate change on exploited marine ecosystems.En prensa2,27