# 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.

**DOI: **http://dx.doi.org/10.7900/jot.2012mar13.1954

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

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