In this paper, we study nonlinear analytic methods for linear contractive operators in Banach spaces. Using these results, we obtain some new strong convergence theorems for commutative families of linear contractive operators in Banach spaces. In the results, the limit points are characterized by sunny generalized nonexpansive retractions.

Under certain hypotheses, diffusion semigroups on commutative L-spaces are known to have an analytic extension for | arg z| < π 2 − arctan |p−2| 2 √ p−1 . In this paper it is shown that semigroups on non-commutative L-spaces have the same extension under suitable conditions. These conditions even lead to a new result in the commutative case. Further, some examples are considered.

We investigate the Lp-spectrum of linear operators defined consistently on Lp(Ω) for p0 ≤ p ≤ p1, where (Ω, μ) is an arbitrary σ-finite measure space and 1 ≤ p0 < p1 ≤ ∞. We prove p-independence of the Lp-spectrum assuming weighted norm estimates. The assumptions are formulated in terms of a measurable semi-metric d on (Ω, μ); the balls with respect to this semi-metric are required to satisfy a...

We consider the weak regularity problem of posed-well-p L linear systems () ∞ < ≤ p 1 in Banach state spaces when its associated unbounded controllers take values in the extrapolated Favard class. We prove that this type of posed-well-p L linear systems are weakly regular and this regularity is output operators independent up to the well-posedness, provided the associated state spaces are non-r...

we give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(c_{omega_1,varphi_1}^*‎ , ‎c_{omega_2,varphi_2}^*)$ on the hilbert space $mathcal{h}$ of analytic functions is supercyclic‎.

We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel’s functional equation and to study asymptotic behavior of such semigroups. The crucial point is that these solutions are univalent functions convex in one direction. In a parallel direction, we find analytic conditions which determine...

This paper is a non exhaustive survey about Hardy spaces defined by semigroups of operators.