enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Banach space - Wikipedia

    en.wikipedia.org/wiki/Banach_space

    In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space.Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space.

  3. List of Banach spaces - Wikipedia

    en.wikipedia.org/wiki/List_of_Banach_spaces

    Tsirelson space, a reflexive Banach space in which neither nor can be embedded. W.T. Gowers construction of a space X {\displaystyle X} that is isomorphic to X ⊕ X ⊕ X {\displaystyle X\oplus X\oplus X} but not X ⊕ X {\displaystyle X\oplus X} serves as a counterexample for weakening the premises of the Schroeder–Bernstein theorem [ 1 ]

  4. Type and cotype of a Banach space - Wikipedia

    en.wikipedia.org/wiki/Type_and_cotype_of_a...

    In functional analysis, the type and cotype of a Banach space are a classification of Banach spaces through probability theory and a measure, how far a Banach space from a Hilbert space is. The starting point is the Pythagorean identity for orthogonal vectors ( e k ) k = 1 n {\displaystyle (e_{k})_{k=1}^{n}} in Hilbert spaces

  5. Stefan Banach - Wikipedia

    en.wikipedia.org/wiki/Stefan_Banach

    Stefan Banach was born on 30 March 1892 at St. Lazarus General Hospital in Kraków, then part of the Austro-Hungarian Empire, into a Góral Roman Catholic family, [4] and was subsequently baptised by his father. [5] [6] Banach's parents were Stefan Greczek and Katarzyna Banach, both natives of the Podhale region.

  6. Banach lattice - Wikipedia

    en.wikipedia.org/wiki/Banach_lattice

    Banach lattices are extremely common in functional analysis, and "every known example [in 1948] of a Banach space [was] also a vector lattice." [1] In particular: ℝ, together with its absolute value as a norm, is a Banach lattice.

  7. Closed range theorem - Wikipedia

    en.wikipedia.org/wiki/Closed_range_theorem

    In the mathematical theory of Banach spaces, the closed range theorem gives necessary and sufficient conditions for a closed densely defined operator to have closed range. The theorem was proved by Stefan Banach in his 1932 Théorie des opérations linéaires.

  8. ba space - Wikipedia

    en.wikipedia.org/wiki/Ba_space

    There is an obvious algebraic duality between the vector space of all finitely additive measures σ on Σ and the vector space of simple functions (() = ()). It is easy to check that the linear form induced by σ is continuous in the sup-norm if σ is bounded, and the result follows since a linear form on the dense subspace of simple functions ...

  9. Approximation property - Wikipedia

    en.wikipedia.org/wiki/Approximation_property

    The construction of a Banach space without the approximation property earned Per Enflo a live goose in 1972, which had been promised by Stanisław Mazur (left) in 1936. [1] In mathematics, specifically functional analysis, a Banach space is said to have the approximation property (AP), if every compact operator is a limit of finite-rank ...