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In this paper we prove that there are hypercyclic (n+1)-tuples of diagonal matrices on Cn and that there are no hypercyclic n-tuples of diagonalizable matrices on Cn. We use the last result to show that there are no hypercyclic subnormal tuples in infinite dimensions. We then show that on real Hilbert spaces there are tuples with somewhere dense orbits that are not dense, but we also give sufficient...
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