Semi-Hilbert space

Semi-Hilbert space

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

* [http://www.unet.univie.ac.at/~a9301647/publications/thesis.ps Optimal Interpolation in Semi-Hilbert Spaces]


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