Continuous Linear Operators On Infinite Quasi-Sobolev Spaces ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$

In this study, the concept of infinite quasi-Sobolev spaces ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$, where m ∈ is considered. These spaces have been proved as quasi-Banach spaces, as well as, Banach spaces, while they neither Hilbert spaces nor quasi-Hilbert spaces. Some kinds of linear operators such as continuous, bounded, closed and completely continuous for operators which map ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$ or ${ {\mathcal L} }_{1}^{m}$ into ${ {\mathcal L} }_{{\rm{\infty }}}^{m}$ are discussed.