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arXiv · 1711.10263

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

Abdullah Aydın
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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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Abdullah Aydın. 2019-12-14. Continuous Operators with Convergence in Lattice-Normed Locally Solid Riesz Spaces. https://arxiv.org/abs/1711.10263

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