ENSIKLOPEDIA Cari Tekan Enter untuk memulai pencarian cepat. Kembali ke Ensiklopedia Arsip Wikipedia Indonesia BK-space BK-spaceSequence space that is Banach In functional analysis and related areas of mathematics, a BK-space or Banach coordinate space is a sequence space endowed with a suitable norm to turn it into a Banach space. All BK-spaces are normable FK-spaces.[1] Examples The space of convergent sequences c , {\displaystyle c,} the space of vanishing sequences c 0 , {\displaystyle c_{0},} and the space of bounded sequences ℓ ∞ {\displaystyle \ell ^{\infty }} under the supremum norm ‖ ⋅ ‖ ∞ . {\displaystyle \|\cdot \|_{\infty }.} [1] The space of absolutely p-summable sequences ℓ p {\displaystyle \ell ^{p}} with p ≥ 1 {\displaystyle p\geq 1} and the norm ‖ ⋅ ‖ p . {\displaystyle \|\cdot \|_{p}.} [1] See also FK-AK space FK-space – Sequence space that is Fréchet Normed space – Vector space on which a distance is definedPages displaying short descriptions of redirect targets Sequence space – Vector space of infinite sequences References 1 2 3 Banas, Jozef; Mursaleen, M. (2014), Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, p. 20, ISBN 9788132218869. vteBanach space topicsTypes of Banach spaces Asplund Banach list Banach lattice Grothendieck Hilbert Inner product space Polarization identity (Polynomially) Reflexive Riesz L-semi-inner product (B Strictly Uniformly) convex Uniformly smooth (Injective Projective) Tensor product (of Hilbert spaces) Banach spaces are: Barrelled Complete F-space Fréchet tame Locally convex Seminorms/Minkowski functionals Mackey Metrizable Normed norm Quasinormed Stereotype Function space Topologies Banach–Mazur compactum Dual Dual space Dual norm Operator Ultraweak Weak polar operator Strong polar operator Ultrastrong Uniform convergence Linear operators Adjoint Bilinear form operator sesquilinear (Un)Bounded Closed Compact on Hilbert spaces (Dis)Continuous Densely defined Fredholm kernel operator Hilbert–Schmidt Functionals positive Pseudo-monotone Normal Nuclear Self-adjoint Strictly singular Trace class Transpose Unitary Operator theory Banach algebras C*-algebras Operator space Spectrum C*-algebra radius Spectral theory of ODEs Spectral theorem Polar decomposition Singular value decomposition Theorems Anderson–Kadec Banach–Alaoglu Banach–Mazur Banach–Saks Banach–Schauder (open mapping) Banach–Steinhaus (Uniform boundedness) Bessel's inequality Cauchy–Schwarz inequality Closed graph Closed range Eberlein–Šmulian Freudenthal spectral Gelfand–Mazur Gelfand–Naimark Goldstine Hahn–Banach hyperplane separation Kakutani fixed-point Krein–Milman Lomonosov's invariant subspace Mackey–Arens Mazur's lemma M. Riesz extension Parseval's identity Riesz's lemma Riesz representation Robinson-Ursescu Schauder fixed-point Sobczyk's theorem Analysis Abstract Wiener space Banach manifold bundle Bochner space Convex series Differentiation in Fréchet spaces Derivatives Fréchet Gateaux functional holomorphic quasi Integrals Bochner Dunford Gelfand–Pettis regulated Paley–Wiener weak Functional calculus Borel continuous holomorphic Measures Lebesgue Projection-valued Vector Weakly / Strongly measurable function Types of sets Absolutely convex Absorbing Affine Balanced/Circled Bounded Convex Convex cone (subset) Convex series related ((cs, lcs)-closed, (cs, bcs)-complete, (lower) ideally convex, (Hx), and (Hwx)) Linear cone (subset) Radial Radially convex/Star-shaped Symmetric Zonotope Subsets / set operations Affine hull (Relative) Algebraic interior (core) Bounding points Convex hull Extreme point Interior Linear span Minkowski addition Polar (Quasi) Relative interior Examples Absolute continuity AC b a ( Σ ) {\displaystyle ba(\Sigma )} c space Banach coordinate BK Besov B p , q s ( R ) {\displaystyle B_{p,q}^{s}(\mathbb {R} )} Birnbaum–Orlicz Bounded variation BV Bs space Continuous C(K) with K compact Hausdorff Hardy Hp Hilbert H Morrey–Campanato L λ , p ( Ω ) {\displaystyle L^{\lambda ,p}(\Omega )} ℓp ℓ ∞ {\displaystyle \ell ^{\infty }} Lp L ∞ {\displaystyle L^{\infty }} weighted Schwartz S ( R n ) {\displaystyle S\left(\mathbb {R} ^{n}\right)} Segal–Bargmann F Sequence space Sobolev Wk,p Sobolev inequality Triebel–Lizorkin Wiener amalgam W ( X , L p ) {\displaystyle W(X,L^{p})} Applications Differential operator Finite element method Mathematical formulation of quantum mechanics Ordinary Differential Equations (ODEs) Validated numerics vteTopological vector spaces (TVSs)Basic concepts Banach space Completeness Continuous linear operator Linear functional Fréchet space Linear map Locally convex space Metrizability Operator topologies Topological vector space Vector space Main results Anderson–Kadec Banach–Alaoglu Closed graph theorem F. Riesz's Hahn–Banach (hyperplane separation Vector-valued Hahn–Banach) Open mapping (Banach–Schauder) Bounded inverse Uniform boundedness (Banach–Steinhaus) Maps Bilinear operator form Linear map Almost open Bounded Continuous Closed Compact Densely defined Discontinuous Topological homomorphism Functional Linear Bilinear Sesquilinear Norm Seminorm Sublinear function Transpose Types of sets Absolutely convex/disk Absorbing/Radial Affine Balanced/Circled Banach disks Bounding points Bounded Complemented subspace Convex Convex cone (subset) Linear cone (subset) Extreme point Pre-compact/Totally bounded Prevalent/Shy Radial Radially convex/Star-shaped Symmetric Set operations Affine hull (Relative) Algebraic interior (core) Convex hull Linear span Minkowski addition Polar (Quasi) Relative interior Types of TVSs Asplund B-complete/Ptak Banach (Countably) Barrelled BK-space (Ultra-) Bornological Brauner Complete Convenient (DF)-space Distinguished F-space FK-AK space FK-space Fréchet tame Fréchet Grothendieck Hilbert Infrabarreled Interpolation space K-space LB-space LF-space Locally convex space Mackey (Pseudo)Metrizable Montel Quasibarrelled Quasi-complete Quasinormed (Polynomially Semi-) Reflexive Riesz Schwartz Semi-complete Smith Stereotype (B Strictly Uniformly) convex (Quasi-) Ultrabarrelled Uniformly smooth Webbed With the approximation property Category vteFunctional analysis (topics – glossary)Spaces Banach Besov Fréchet Hilbert Inner product Normed Nuclear Schwartz Sobolev Topological vector Properties Barrelled Complete Dual (Algebraic / Topological) Locally convex Reflexive Separable Theorems Hahn–Banach Riesz representation Closed graph Uniform boundedness principle Kakutani fixed-point Krein–Milman Min–max Gelfand–Naimark Banach–Alaoglu Operators Adjoint Bounded Compact Hilbert–Schmidt Normal Nuclear Trace class Transpose Unbounded Unitary Algebras Banach algebra C*-algebra Spectrum of a C*-algebra Operator algebra Group algebra of a locally compact group Von Neumann algebra Open problems Invariant subspace problem Mahler's conjecture Applications Hardy space Spectral theory of ordinary differential equations Heat kernel Index theorem Calculus of variations Functional calculus Integral linear operator Jones polynomial Topological quantum field theory Noncommutative geometry Riemann hypothesis Distribution (or Generalized functions) Advanced topics Approximation property Balanced set Choquet theory Weak topology Banach–Mazur distance Tomita–Takesaki theory Category This mathematical analysis–related article is a stub. 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