noun
Hilbert space
A complete inner product space; a fundamental concept in functional analysis and quantum mechanics.
量子力学では、状態はヒルベルト空間のベクトルで表される。
In quantum mechanics, states are represented by vectors in a Hilbert space.
A Banach space is a complete normed vector space; every Hilbert space is a Banach space, but not conversely.
Named after the German mathematician David Hilbert. The term was introduced by John von Neumann in the context of quantum mechanics.