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Journal of Operator Theory

Volume 71, Issue 2,  Spring  2014  pp. 303-326.

Strong dual factorization property

Authors:  Denis Poulin
Author institution: Mathematics Department, University of Alberta, Edmonton, T6G 2G1, Canada

Summary:  Let $A$ be a Banach algebra. We give a new characterization of the property $A^*=A^*A$, called the left strong dual factorization property when one assumes that $A$ has a bounded approximate identity. Without the assumption of the existence of a bounded approximate identity, we prove that this property implies the equivalence between the given norm of $A$ and the norm inherited from $RM(A)$, the right multiplier algebra of $A$. Secondly, we present a complete description of the strong topological centres of $N_{\alpha}(E)$ of $\alpha$-nuclear operators on a Banach space $E$. Using this description, we characterize the Banach spaces $E$ such that $N_{\alpha}(E)$ has the left and right strong dual factorization property.

Keywords: approximable operator, dual factorization property, Banach algebra, nuclear operator

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