We use techniques of proof mining to obtain a computable and uniform rate metastability (in the sense Tao) for mean ergodic theorem finite number commuting linear contractive operators on uniformly convex Banach space.

We consider non-conservative positive semigroups and obtain necessary sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements provides quantitative estimates spectral gap, complementing Krein–Rutman theorems generalizing probabilistic approaches. The proof is based on a non-homogenous h $h$ -transform semigro...