PACKING CONSTANTS IN ORLICZ-LORENTZ SEQUENCE SPACES

We discussed the upper and lower bounds of packing constants in Orlicz-Lorentz sequence spaces equipped with both the Luxemburg norm and the Orlicz norm. Provided Phi is an element of Delta(2)(0), we showed that the Kottman constant of and lambda(Phi,omega) and lambda(o)(Phi,omega) satisfies max{1/alpha(Phi)(0), 1/alpha'(Phi,omega)} <= K(lambda(Phi,omega)) <= 1/(alpha) over tilde (Phi,omega), max{1/alpha(Phi)(0), 1/alpha ''(Phi,omega)} <= K(lambda(o)(Phi,omega)) <= 1/alpha*(Phi). As a corollary, the packing constant of Lorentz space lambda(p,omega) is 1/(1 + 2(1-1/p)). The packing constants of Orlicz spaces were studied by many researchers. However, there are few results on geometric constants of Lorentz spaces as well as Orlicz-Lorentz spaces. In this paper, we shall study the packing constant in OrliczLorentz sequence spaces lambda(Phi,omega) and lambda(o)(Phi,omega) (equipped with the Luxemburg norm and the Orlicz norm respectively). We will obtain the nontrivial lower and upper bounds of the Kottman constant. Both the technical ideas and the computational methods are practical and can be employed to estimate some other geometric constants in Orlicz-Lorentz spaces.