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Or is it only theoretical.
Hilbert space is a mathematical concept. It exists the same way that sets exist, or vectors, or the number line.Or is it only theoretical.
Hilbert space is a purely mathematical concept, generalized Euclidean space. Much of quantum theory uses Hilbert space as part of the development.There are a great many examples of Hilbert spaces. They do exist. You might want to ask if a particular space you are interested in is a Hilbert space.
Yes. Hilbert spaces are more the rule than the exception in spaces that we study. There are examples everywhere. The only reasonable question is whether a particular unusual space is a Hilbert space. So the OP should specify what space he is asking about.Hilbert space is a purely mathematical concept, generalized Euclidean space. Much of quantum theory uses Hilbert space as part of the development.
The real numbers and the complex plane are both Hilbert spaces.Or is it only theoretical.
Although it might simply be a matter of definition, but Hilbert space is usually defined as an infinite dimensional analog of n dimensional Euclidean space.The real numbers and the complex plane are both Hilbert spaces.
The opening post asked if a Hilbert Space exist so I gave the simplest ones, and BTW:Although it might simply be a matter of definition, but Hilbert space is usually defined as an infinite dimensional analog of n dimensional Euclidean space.