In functional analysis, a field of mathematics, the Banach–Mazur theorem is a theorem roughly stating that most well-behaved normed spaces are subspaces...

In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace...

Banach–Steinhaus theorem, the Banach–Mazur game, the Banach–Alaoglu theorem, Banach-Saks property, and the Banach fixed-point theorem. Stefan Banach was born...

Banach–Mazur theorem, every Banach space is isometrically isomorphic to a subspace of some C ( K ) . {\displaystyle C(K).} For every separable Banach...

Approximation property Banach–Mazur theorem Banach–Mazur game Compact operator Gelfand–Mazur theorem Mazur–Ulam theorem Schauder basis Stanisław Mazur at the Mathematics...

C ( [ 0 , 1 ] ) {\displaystyle C([0,1])} . The Banach–Mazur theorem asserts that any separable Banach space is isometrically isomorphic to a closed linear...

operator theory, the Gelfand–Mazur theorem is a theorem named after Israel Gelfand and Stanisław Mazur which states that a Banach algebra with unit over the...

In the mathematical study of functional analysis, the Banach–Mazur distance is a way to define a distance on the set Q ( n ) {\displaystyle Q(n)} of n...

analysis and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space...

theory, a Banach–Mazur game is a topological game played by two players, trying to pin down elements in a set (space). The concept of a Banach–Mazur game is...

Mazur's theorem may refer to: Ascoli–Mazur theorem, or Mazur's theorem, a corollary of the Hahn–Banach separation theorem in functional analysis Mazur's...

Fredholm's theorem (linear algebra) Analytic Fredholm theorem (functional analysis) Banach–Alaoglu theorem (functional analysis) Banach–Mazur theorem (functional...

algebra is the complexes. (This is known as the Gelfand–Mazur theorem.) Every unital real Banach algebra with no zero divisors, and in which every principal...

In mathematics, the Mazur–Ulam theorem states that if V {\displaystyle V} and W {\displaystyle W} are normed spaces over R and the mapping f : V → W {\displaystyle...

Arzelà–Ascoli theorem Banach–Alaoglu theorem Measure of non-compactness Banach–Mazur theorem Bounded linear operator Continuous linear extension Compact operator...

ISBN 0-486-68735-X Kleiber, Martin; Pervin, William J. (1969). "A generalized Banach-Mazur theorem". Bull. Austral. Math. Soc. 1 (2): 169–173. doi:10.1017/S0004972700041411...

In mathematics, the Bishop–Phelps theorem is a theorem about the topological properties of Banach spaces named after Errett Bishop and Robert Phelps,...

Banach norm Banach–Alaoglu theorem Banach–Mazur compactum Banach–Mazur game Banach–Mazur theorem Banach–Ruziewicz problem Banach-Saks theorem Banach-Schauder...

Banach–Stone theorem is a classical result in the theory of continuous functions on topological spaces, named after the mathematicians Stefan Banach and...

"distortion" (in Gromov's terminology for the Lipschitz category; cf. Banach–Mazur distance). Low-dimensional problems have lower computational complexity...

{\text{for every}}\ x\in E.} In terms of the multiplicative Banach-Mazur distance d the theorem's conclusion can be formulated as: d ( E ,   ℓ k 2 ) ≤ 1 +...

general, commutative Banach algebra case.) For any such m the quotient algebra A/m is one-dimensional (by the Gelfand-Mazur theorem), and therefore any...

identity 1A such that ║1A║ = 1. Banach algebra Composition algebra Division algebra Gelfand–Mazur theorem Hurwitz's theorem (composition algebras) "Normed...

{\displaystyle Y.} Then there is a Banach–Mazur game M Z ( X , Y , W ) . {\displaystyle MZ(X,Y,{\mathcal {W}}).} In the Banach–Mazur game, two players, P {\displaystyle...

mathematics, the Goldstine theorem, named after Herman Goldstine, is stated as follows: Goldstine theorem. Let X {\displaystyle X} be a Banach space, then the image...

y_{k}-x\rVert \to 0} . Banach–Alaoglu theorem – Theorem in functional analysis Bishop–Phelps theorem Eberlein–Šmulian theorem – Relates three different...

theorem is an important step in deciding which spaces of weak solutions to use in solving a PDE. Banach–Alaoglu theorem Bishop–Phelps theorem Mazur's...

methods in nonlinear analysis. Banach–Schauder theorem Schauder basis Schauder estimates Schauder fixed point theorem List of Polish mathematicians Kuratowski...

called Banach-Saks sequences. The concept is named after Polish mathematicians Stefan Banach and Stanisław Saks, who extended Mazur's theorem, which states...

category theorem Nowhere dense Baire space Banach–Mazur game Meagre set Comeagre set Compact space Relatively compact subspace Heine–Borel theorem Tychonoff's...