Dynamics of a Compact Operator

الملخص EN

Let T:X→X be a compact linear (or more generally affine) operator from a Banach space into itself.

For each x∈X, the sequence of iterates Tnx, n=0, 1, … and its averages (1/k)∑k=0nTk−1x,n=0, 1, … are either bounded or approach infinity.