Partial inner product spaces. I. General properties
(1976) Journal of Functional Analysis — Vol. 23, n° 4, p. 369-378 (1976)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- Vector spaces V with a natural “partial inner product” are very common in analysis and in mathematical physics. In this series of papers, we study them on their own terms; the only input is the domain of the partial inner product and the partial inner product itself. Our main assumption is that the linear forms associated to “infinitely good elements” of V, separate points in V. We show in this paper that V carries then a well-defined “self-dual” structure. Examples are discussed.
- Affiliations
Centre de Physique Théorique, Marseille CPT
Citations
Antoine, J.-P., & Grossmann, A. (1976). Partial inner product spaces. I. General properties. Journal of Functional Analysis, 23(4), 369-378. https://doi.org/10.1016/0022-1236(76)90063-X (Original work published 1976)