Transitivity for linear operators on a Banach space
Volume 132 / 1999
Studia Mathematica 132 (1999), 239-243
DOI: 10.4064/sm-132-3-239-243
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.
