Hyperreflexivity of the space of module homomorphisms between non-commutative L-spaces

Alaminos, J.; Extremera, J.; Godoy, M. L. C.; Villena, A. R.

doi:10.1016/j.jmaa.2021.124964

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“…From [11,Corollary 1.3], it follows that each C * -algebra A is strongly zero product determined, has the strong property B, and α A , β A ≤ 8. It is shown in [7] that each group algebra has the strong property B and so (by Corollary 2.2 below) it is also strongly zero product determined.…”

Section: Introductionmentioning

confidence: 99%

Strongly zero product determined Banach algebras

Alaminos¹,

Extremera²,

Godoy³

et al. 2021

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C * -algebras, group algebras, and the algebra A(X) of approximable operators on a Banach space X having the bounded approximation property are known to be zero product determined. We are interested in giving a quantitative estimate of this property by finding, for each Banach algebra A of the above classes, a constant α with the property that for every continuous bilinear functional ϕ : A × A → C there exists a continuous linear functional ξ on A such that sup a = b =1 |ϕ(a, b) − ξ(ab)| ≤ α sup a = b =1, ab=0 |ϕ(a, b)|.

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Section: Introductionmentioning

confidence: 99%