Year: 2017
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Aydın, Abdullah
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2782428882