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Abstract

Let G be the multiplicative group of invertible elements of E(X), the algebra of all bounded linear operators on a Banach space X. In 1945 Mackey showed that if $x_1,…,x_n$ and $y_1,…,y_n$ are any two sets of linearly independent elements of X with the same number of items, then there exists T ∈ G so that $T(x_k) = y_k$, $k = 1,…,n$. We prove that some proper multiplicative subgroups of G have this property.