Continuous Operators with Convergence in Lattice-Normed Locally Solid Riesz Spaces

2017/11/28 by Abdullah Aydın, Aydın, Abdullah
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.1711.10263

openalex publication_date 2017/11/28 · openalex created_date 2018/01/12 · openalex updated_date 2026/07/28

Abstract

A linear operator T between two lattice-normed locally solid Riesz spaces is said to be p_τ-continuous if, for any p_τ-null net (x_α), the net (Tx_α) is p_τ-null, and T is also said to be p_τ-bounded operator if it sends p_τ-bounded subsets to p_τ-bounded subsets. They are generalize several known classes of operators such as continuous, order continuous, p-continuous, order bounded, p-bounded operators, etc. We also study up_τ-continuous operators between lattice-normed locally solids Riesz spaces.

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