Spectral radius of weighted composition operators in LP-spaces

We prove that for the spectral radius of a weighted composition operator aT(alpha) acting in the space L-P(X,B,mu), the following variational principle holds: ln r(aT(alpha)) = max (1)(v is an element of M alpha,e)integral(X)ln vertical bar a(sic)dv, where X is a Hausdorff compact space, alpha: X -> X is a continuous mapping preserving a Borel measure mu with supp mu = X, M-alpha,e(1) is the set of all alpha-invariant ergodic probability measures on X, and (sic) X -> R is a continuous and B-infinity-measurable function, where B-infinity = boolean AND(infinity)(n=0) alpha(-n)(B) This considerably extends the range of validity of the above formula, which was previously known in the case when a is a homeomorphism