2009
DOI: 10.4064/sm192-2-3
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Factorizing multilinear operators on Banach spaces, C*-algebras and JB*-triples

Abstract: In recent papers, the Right and the Strong * topologies have been introduced and studied on general Banach spaces. We characterize different types of continuity for multilinear operators (joint, uniform, etc.) with respect to the above topologies. We also study the relations between them. Finally, in the last section, we relate the joint Strong *-to-norm continuity of a multilinear operator T defined on C *-algebras (respectively, JB *-triples) to C *-summability (respectively, JB *-triple-summability).

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“…Jointly w-right-norm continuous multilinear operators have been studied in [22,30] and [37]. A multilinear operator T : The polarization formula (4.1) guarantees that an m-homogeneous polynomial P is w-right-norm continuous if and only if its generating multilinear operator is jointly w-right-norm continuous (at 0) if and only if P is w-right-norm continuous at 0.…”
Section: W-right-norm Continuous Holomorphic Mappingsmentioning
confidence: 99%
“…Jointly w-right-norm continuous multilinear operators have been studied in [22,30] and [37]. A multilinear operator T : The polarization formula (4.1) guarantees that an m-homogeneous polynomial P is w-right-norm continuous if and only if its generating multilinear operator is jointly w-right-norm continuous (at 0) if and only if P is w-right-norm continuous at 0.…”
Section: W-right-norm Continuous Holomorphic Mappingsmentioning
confidence: 99%