Semi-Hilbert space

Short description: Mathematical concept

In mathematics, a semi-Hilbert space is a generalization of a Hilbert space in functional analysis, in which, roughly speaking, the inner product is required only to be positive semi-definite rather than positive definite, so that it gives rise to a seminorm rather than a vector space norm.

The quotient of this space by the kernel of this seminorm is also required to be a Hilbert space in the usual sense.

## References

* Optimal Interpolation in Semi-Hilbert Spaces

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