7: Hilbert Spaces Flashcards
1
Q
a Hilbert space is an inner-product space that is ___ wrt norm
A
complete
2
Q
Orthogonal complement of AcH is a ___ subspace of H
A
closed
3
Q
point y closest to x is the unique element such that x-y is ___ to a closed subspace of H
A
orthogonal
4
Q
a ___ of H is an orthonormal basis of H
A
complete orthonormal subset
5
Q
every hilbert space has an ___ basis
A
orthonormal
6
Q
a partically ordered set that has upper bounds for its totally ordered subsets has a ___
A
maximal element
7
Q
a hilbert space is separable iff it has a ___ basis
A
countable orthonormal
