Linear Operators: General theory |
From inside the book
Results 1-3 of 61
Page 136
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Page 143
... determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel - Stieltjes measure determined by f . If u is either the Borel - Stieltjes or the Lebesgue - Stieltjes measure ...
... determined by a func- tion f of bounded variation on a finite or infinite interval is the Le- besgue extension of the Borel - Stieltjes measure determined by f . If u is either the Borel - Stieltjes or the Lebesgue - Stieltjes measure ...
Page 455
... determined by GE . F = We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in G1 ...
... determined by GE . F = We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in G1 ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ