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An ℰp space is a product of
finite-dimensional cp spaces with a weighted lp norm on the product. The first
theorem of this paper yields an isometric embedding of ℰp into an appropriate cp
space. From this theorem, known results about cp are used to deduce, among other
things, the Clarkson inequalities for ℰp,1 < p < ∞, and hence, the uniform convexity
of ℰp for 1 < p < ∞.
The second theorem charaeterizes the conjugate space of ℰp for 0 < p < 1. This
result is then used to describe some spaces of multipliers. Let 𝒜 and ℬ be ℰp spaces,
1 ≦ p ≦∞, or ℰ0. The spaces ℳ(𝒜,ℬ) of multipliers from 𝒜 to ℬ have previously
been identified with certain subspaces of ℰ(I) and determined precisely in some cases.
The third theorem is a complete description of these multiplier spaces: the cases
0 < p < 1 are included and the spaces ℳ(𝒜,ℬ) are determined precisely for all pairs
𝒜,ℬ.
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