In mathematics, particularly functional analysis, the Dunford–Schwartz theorem, named after Nelson Dunford and Jacob T. Schwartz, states that the averages of powers of certain norm-bounded operators on L 1 converge in a suitable sense. Statement of the theorem

Inom funktionalanalys, en del av matematiken, är Dunford–Schwartzs sats, uppkallad efter Nelson Dunford och Jacob T. Schwartz, en sats om konvergensen av medeltal av potenser av vissa operatorer över L 1.Satsen säger följande: [1] Låt vara en linjär operator från till med ‖ ‖ och ‖ ‖.Då existerar = nästan överallt för alla . [2]Källor

In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous. Many standard Banach spaces have this property, most notably, the space C of continuous functions on a compact space and the space …

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Dunford – Schwartz tétel - Dunford–Schwartz theorem A Wikipédiából, a szabad enciklopédiából A matematika , különösen a funkcionális elemzés , a Dunford-Schwartz tétel elnevezett Nelson Dunford és Jacob T. Schwartz , kimondja, hogy az átlagai hatásköre bizonyos norm- korlátos operátorok az L 1 Converge egy megfelelő ...

The theorem asserts that if the normed space R is complete (thus R is a Hilbert space), then any sequence {} that has finite norm defines a function f in the space R. The function f is defined by f = lim n → ∞ ∑ k = 0 n c k φ k , {\displaystyle f=\lim _{n\to \infty }\sum _{k=0}^{n}c_{k}\varphi _{k},} limit in R -norm.

Jack Schwartz... .: Yale University , 1951 See also • Dunford - Schwartz theorem Notes •^ a b Markoff , John ( 3 ... Nelson Dunford... Dunford decomposition , Dunford – Pettis property , and Dunford - Schwartz theorem bear his name . He studied mathematics at the University ...

Properties. All three spaces are complete (they are Banach spaces) with respect to the same norm defined by the total variation, and thus () is a closed subset of (), and () is a closed set of () for Σ the algebra of Borel sets on X.The space of simple functions on is dense in ().. The ba space of the power set of the natural numbers, ba(2 N), is often denoted as simply and is isomorphic …

(Dunford & Schwartz 1958, §IV.6.3) Positive linear functionals on () correspond to (positive) regular Borel measures on , by a different form of the Riesz representation theorem. (Rudin 1966, Chapter 2) If is infinite, then () is not reflexive, nor is it weakly complete. ...