@misc{10481/84697,
year = {2023},
month = {7},
url = {https://hdl.handle.net/10481/84697},
abstract = {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).},
organization = {Universidad de Granada/CBUA},
organization = {MCIN/AEI/
	PID2021-122126NB-C31},
organization = {"ERDF A way of making Europe"},
organization = {Junta de Andalucia
	FQM375,
	
	PY20_00255},
organization = {MAG-Mariade Maeztu
	CEX2020-001105-M/AEI/10.13039/501100011033},
organization = {National Natural Science Foundation of China (NSFC)
	12171251},
publisher = {Springer Nature},
keywords = {JB∗-algebra},
keywords = {σ-unital},
keywords = {Multipliers},
keywords = {J-strict topology},
keywords = {Jordan homomorphism},
keywords = {Triple homomorphism},
keywords = {Orthogonality preserver},
keywords = {Extension of Jordan∗-epimorphisms},
title = {On the strict topology of the multipliers of a JB∗-algebra},
doi = {10.1007/s13398-023-01476-w},
author = {Fernández Polo, Francisco José and Garcés, Jorge J. and Li, Lei and Peralta Pereira, Antonio Miguel},
}