In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,rese...In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.展开更多
We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on ...We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided.展开更多
文摘In this article,we consider Orlicz-Lorentz sequence spaces equipped with the Orlicz norm(λ_(φ,ω),‖·‖_(φ,ω)^(O))generated by any Orlicz function and any non-increasing weight sequence.As far as we know,research on such a general case is conducted for the first time.After showing that the Orlicz norm is equal to the Amemiya norm in general and giving some important properties of this norm,we study the problem of existence of order isomorphically isometric copies of l∞in the space(λ_(φ,ω),‖·‖_(φ,ω)^(O))and we find criteria for order continuity and monotonicity properties of this space.We also find criteria for monotonicity properties of n-dimensional subspaces λ_(φ,ω)^(n)(n≥2)and the subspace(λ_(φ,ω))_(a) of order continuous elements of λ_(φ,ω).Finally,as an immediate consequence of the criteria considered in this article,the properties of Orlicz sequence spaces equipped with the Orlicz norm are deduced.
文摘We present here that F（E,F）, the space of all r-compact operators from E into F, is a generalised sublattice of L^r（E, F） for arbitary Banach lattices E and F, and that the characterization of the regular norm on F（E, F） is order continuous. Some conditions for F（E, F） to be a KB-space or a band in .L（E, F） are also provided.
