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- Weighted Subsequential ergodic theorems on Orlicz spaces(arXiv)
Author : Panchugopal Bikram, Diptesh Saha
Abstract : For a semifinite von Neumann algebra M, individual convergence of subsequential, mathcal{Z}(M) (center of M) valued weighted ergodic averages are studied in noncommutative Orlicz spaces. In the process, we also derive a maximal ergodic inequality corresponding to such averages in noncommutative L^p~ (1 leq p < infty) spaces using the weak (1,1) inequality obtained by Yeadon.
2.Convergence results in Orlicz spaces for sequences of max-product Kantorovich sampling operators (arXiv)
Author : Lorenzo Boccali, Danilo Costarelli, Gianluca Vinti
Abstract : In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions defined on both bounded intervals and on the whole real axis has been considered. Here, under suitable assumptions on the kernels, considered in order to define the operators, we are able to establish a modular convergence theorem for these sampling-type operators. As a direct consequence of the main theorem of this paper, we obtain that the involved operators can be successfully used for approximation processes in a wide variety of functional spaces, including the well-known interpolation and exponential spaces. This makes the Kantorovich variant of max-product sampling operators suitable for reconstructing not necessarily continuous functions (signals) belonging to a wide range of functional spaces. Finally, several examples of Orlicz spaces and of kernels for which the above theory can be applied are presented.