On the strict topology of the multipliers of a JB∗-algebra Fernández Polo, Francisco José Garcés, Jorge J. Li, Lei Peralta Pereira, Antonio Miguel JB∗-algebra σ-unital Multipliers J-strict topology Jordan homomorphism Triple homomorphism Orthogonality preserver Extension of Jordan∗-epimorphisms 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). 2023-09-28T06:56:46Z 2023-09-28T06:56:46Z 2023-07-13 journal article Fernández-Polo, F.J., Garcés, J.J., Li, L. et al. On the strict topology of the multipliers of a JB∗-algebra. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 146 (2023). [https://doi.org/10.1007/s13398-023-01476-w] https://hdl.handle.net/10481/84697 10.1007/s13398-023-01476-w eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional Springer Nature