Hilbert space
Noun
Meaning
a metric space that is linear and complete and (usually) infinite-dimensional
Source: WordNetHypernyms
Related terms
Examples
Quantum phenomena do not occur in a Hilbert space. They occur in a laboratory.
My real speciality is the mathematical analysis of Hilbert Space operators. But this was no time to come on like an ivory-tower idealist.
The traditional "cosmological” Multiverse considers that there might be physical realms inaccessible to us due to their separation in space-time. The quantum Multiverse arises from entities that occupy the same space-time, but are distant in Hilbert space – or in the jargon, decoherent.
A basis of a Hilbert space is not the same thing as a basis in the sense of linear algebra above.
A C*-algebra is a complex algebra A of continuous linear operators on a complex Hilbert space with two additional properties: * A is a topologically closed set in the norm topology of operators.
A Banach space isomorphic to all its infinite-dimensional closed subspaces is isomorphic to a separable Hilbert space.