On the convergence sets of operator sequences on spaces of homogeneous type

2023/10/01 by G. A. Karagulyan, Karagulyan, Grigori A.
Mathematics · #Approximation Theory and Sequence Spaces #Advanced Banach Space Theory #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2310.00621

Abstract

We consider sequences of operators U_n:L¹(X)→ M(X), where X is a space of homogeneous type. Under certain conditions on the operators U_n we give a complete characterization of convergence (divergence) sets of functional sequences U_n(f), where f∈ L^p(X), 1≤ p≤ ∞. The results are applied to characterize convergence sets of some specific operator sequences in classical analysis.

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