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A linear operator $T$ between two vector lattices normed by locally solidRiesz spaces is said to be $p_\tau$-continuous if, for any $p_\tau$-null net$(x_\alpha)$, the net $(Tx_\alpha)$ is $p_\tau$-null, and $T$ is said to be$p_\tau$-bounded operator if it sends $p_\tau$-bounded subsets to$p_\tau$-bounded subsets. Also, $T$ is called $p_\tau$-compact if, for any$p_\tau$-bounded net $(x_\alpha)$, the net $(Tx_\alpha)$ has a$p_\tau$-convergent subnet. They generalize several known classes of operatorssuch as norm continuous, order continuous, $p$-continuous, order bounded,$p$-bounded, compact and AM-compact operators. We study the general propertiesof these operators.

Compact-Like Operators in Vector Lattices Normed by Locally Solid Lattices