On self-polar Hilbertian norms on (indefinite) inner product spaces

Considering a non-degenerate (possibly indefinite) inner product space with complete Hilbertian majorant, the self-polar Hilbertian majorants, which are suitable generalizations of the canonical norm on a pre-Hilbert space, are characterized by an operator equation involving the Gram operator. Among the self-polar Hilbertian norms, both the interesting class of pseudo-decomposition norms and the generic decomposition majorant are distinguished and investigated. Furthermore, characterizations and constructions for pseudo-decomposition majorants, decomposition majorants and the generic decomposition majorant are given.