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

A linear operator $T$ between two lattice-normed locally solid Riesz spaces is said to be $p_{\tau }$-continuous if, for any $p_{\tau }$-null net $(x_{\alpha })$, the net $(T{x}_{\alpha })$ is $p_{\tau }$-null, and $T$ is also said to be $p_{\tau }$-bounded operator if it sends $p_{\tau }$-bounded subsets to $p_{\tau }$-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 $u{p}_{\tau }$-continuous operators between lattice-normed locally solids Riesz spaces.