DOI: 10.68381/jca17012 ISSN: 0944-6532
On the Lower Bounds of Kottman Constants in Orlicz Function Spaces
Z. D. Ren
Let
L^{(\Phi)}(\Omega)
L
(
Φ
)
(
Ω
)
and
L^{\Phi}(\Omega)
L
Φ
(
Ω
)
be the Orlicz function spaces defined by an
N
N
-function
\Phi
Φ
, equipped with the gauge norm and the Orlicz norm respectively, where
\Omega=[0,1]
Ω
=
[
0
,
1
]
or
[0,\infty)
[
0
,
∞
)
. The Kottman constants
K(L^{(\Phi)}(\Omega))
K
(
L
(
Φ
)
(
Ω
)
)
and
K(L^{\Phi}(\Omega))
K
(
L
Φ
(
Ω
)
)
were discussed by M. M. Rao and the author in Chapter 5 of their book “Applications of Orlicz Spaces” [Marcel Dekker Inc., New York, 2002]. The author obtains some improvments on the lower bounds of these constants in Section 2 (Theorems 1 and 2). Several examples are given in Section 3 which will be used to make comments upon the papers of Y. Q. Yan [On the exact value of packing spheres in a class of Orlicz function spaces, J. Convex Analysis 11(2) (2004) 391–400], and J. Han and X. L. Li [Exact value of packing spheres constant in class of Orlicz function spaces (in Chinese), J. Tongji Univ. 30(7) (2002) 895–899].