On the completed hull of non-degenerate inner product spaces (Q6123780)

Summary: Motivated by applications to general QFT, the completed hulls of non-degenerate inner product spaces \(E, (\cdot, \cdot)\) are considered. In order to decide whether or not \(\tilde{E}\) endowed with the continuously extended inner product \((\cdot, \cdot)^{\sim}\) is non-degenerate, the concept of c-linked l.c. topologies \(\tau\) is introduced, and it is shown that \(\tilde{E}, (\cdot, \cdot)^{\sim}\) is non-degenerate if and only if \(\tau\) is c-linked to some minimal majorant. Further, the concepts of quasi-decomposable inner product spaces and quasi-decomposition norms are introduced, and it is shown that \(\tilde{E}, (\cdot, \cdot)^{\sim}\) is a Krein space.