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As a consequence, each $A\\in \\Sigma(X)$ is an orbit of a hypercyclic operator on $X$. Furthermore, every countably dimensional normed space supports a hypercyclic operator.\n  We show that for a separable infinite dimensional Fr\\'echet space $X$, $GL(X)$ acts transitively on $\\Sigma(X)$ if and only if $X$ possesses a continuous norm. 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