The Packing Spheres Constant for a Class of Separable Orlicz Function Spaces

Xisheng Yu
2009 Journal of Mathematics Research  
Few results have been obtained on the packing spheres constant or exact formula for separable Orlicz function spaces (Yang, 2002 , P.895-899, Ye, 1987. In this paper, by using the continuity of ideal space norm, we firstly proved that simple function class is dense in L * Φ function space. This is a necessary condition of interpolation theorem. Hence, the exact value of packing sphere for a class of sparable Orlicz function spaces (with two kinds of norm) is obtained. Secondly, for the space L
more » ... y, for the space L * Φ [0, 1] discussed in (Yang, 2002, P.895-899), we propose the following conjecture: the L * Φ [0, 1] space is actually the L p [0, 1] space, therefore, the results obtained there is actually the proved results in L p space.
doi:10.5539/jmr.v1n2p21 fatcat:midleejbcfbulbla4cddwkdjn4