Explore: Hilbert Spaces

Euclidean vector spaces, examples of Hilbert spaces include spaces of square-integrable functions, spaces of sequences, Sobolev spaces consisting of generalized

the spectral theorem for unbounded operators on Hilbert space can be formulated. "Rigged Hilbert spaces are well known as the structure which provides

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

kernel Hilbert spaces that are spaces of analytic functions. Let X {\displaystyle X} be an arbitrary set and H {\displaystyle H} a Hilbert space of real-valued

quantum mechanics, the projective Hilbert space or ray space P ( H ) {\displaystyle \mathbf {P} (H)} of a complex Hilbert space H {\displaystyle H} is the set

mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an

Euclidean spaces from other spaces that were later considered in physics and modern mathematics. Ancient Greek geometers introduced Euclidean space for modeling

taken as operating on a Hilbert space, but the same notion serves to define the concept of isomorphism between Hilbert spaces. Definition 1. A unitary

integers). The construction may also be extended to cover Banach spaces and Hilbert spaces. See the article decomposition of a module for a way to write a module

linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does not define the notion of "space" itself. A space consists of selected mathematical