Some Properties of
NSupercyclic Operators

Paul S. Bourdon, Nathan S. Feldman,
and Joel H. Shapiro

Studia Mathematica
165 (2) (2004) 135137


Abstract:
We call a continuous linear operator T on a Hausdorff
topological vector space "Nsupercyclic", there is
an N dimensional subspace whose Torbit is dense. We show that
such an operator can have at most N eigenvalues, counting geometric
multiplicity. We show further that Nsupercyclicity cannot occur
nontrivially in the finite dimensional setting: the orbit of
an N dimensional subspace cannotbe dense in an N+1 dimensional
space. Finally, we show that a subnormal operator on an infinitedimensional
Hilbert space can never be Nsupercyclic. 
Download .pdf file (268 KB) 
