Abstract
Given a complex Banach space X, we denote by L(X) the algebra of all linear bounded operators on it. For ε>0, let rε(T) denote the ε−pseudospectral radius of T∈L(X). For an infinite-dimensional space X, we characterize surjective maps φ:L(X)→L(X) such that rε(φ(T1)φ(T2))=rε(T1T2) for all T1,T2∈L(X). An analogous result is obtained in the finite-dimensional case, with no surjectivity assumption on the map φ.
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