Definition of Hilbert space in English:

Hilbert space


  • An infinite-dimensional analogue of Euclidean space.

    • ‘His theorem, now called the Riesz - Fischer theorem, which he proved in 1907, is fundamental in the Fourier analysis of Hilbert space.’
    • ‘In 1943 he proved the Gelfand Naimark theorem on self-adjoint algebras of operators in Hilbert space.’
    • ‘In short, to have any hope of understanding what a Hilbert space is, you must learn and digest a whole hierarchy of lower-level concepts first.’
    • ‘They showed that these rings could always be represented as a ring of linear operators on a Hilbert space.’
    • ‘He took various ideas of Hilbert on integral equations and combined these into the concept of a Hilbert space around 1905.’


Early 20th century: named after David Hilbert (1862–1943), German mathematician.


Hilbert space

/ˈhɪlbət speɪs/