Abstract: Let A be a bounded linear operator on a Banach lattice B.In the case B
is an AL or AM-space, we show that if there exists a positive unit vector e
which is invariant for A, then there
exists the largest subspace Lof Bwhich contains e
and satisfies the property that the sequence converges
to e with respect to the norm in Bfor all positive unit
vectors f in the subspace
L. These results
are Banach lattice version of the property of operators associated with chaotic
maps.
Keywords and phrases: chaotic map, Perron-Frobenius operator.
