Vol. 35, No. 1, 1970

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On a certain generalization of p spaces

A. Jeanne LaDuke

Vol. 35 (1970), No. 1, 155–168

An p 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 p into an appropriate cp space. From this theorem, known results about cp are used to deduce, among other things, the Clarkson inequalities for p,1 < p < , and hence, the uniform convexity of p for 1 < p < .

The second theorem charaeterizes the conjugate space of p for 0 < p < 1. This result is then used to describe some spaces of multipliers. Let 𝒜 and be p spaces, 1 p , or 0. The spaces (𝒜,) of multipliers from 𝒜 to have previously been identified with certain subspaces of (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 (𝒜,) are determined precisely for all pairs 𝒜,.

Mathematical Subject Classification
Primary: 46.35
Received: 21 January 1970
Published: 1 October 1970
A. Jeanne LaDuke