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A vector space equipped with an indefinite inner product is investigated. Selfpolar norms on the space are studied and an operator description for quadratic selfpolar norms is developed when the space allows a Hilbert space topology making the indefinite inner product continuous. The selfpolar norms corresponding to a quasi-decomposition of the space are characterised in terms of the operator description and sufficient conditions for topological equivalence are given. §

Self-polar norms on an indefinite inner product space