Linear Operators: General theory |
From inside the book
Results 1-3 of 73
Page 186
... measure μ of Lemma 1 is countably additive on Ø . Consequently , the restriction of u to the o - field generated by ... positive measure spaces ( $ 1 , 21 , μ1 ) and ( S2 , Z2 , μ2 ) . For each E in E and s2 in S , the set E ( 82 ) ...
... measure μ of Lemma 1 is countably additive on Ø . Consequently , the restriction of u to the o - field generated by ... positive measure spaces ( $ 1 , 21 , μ1 ) and ( S2 , Z2 , μ2 ) . For each E in E and s2 in S , the set E ( 82 ) ...
Page 212
... positive measure defined on the o - field of Borel sets of a compact metric space S. A set ACS is said to be covered in the sense of Vitali by a family F of closed sets if each Fe F has positive μ - measure and there is a positive ...
... positive measure defined on the o - field of Borel sets of a compact metric space S. A set ACS is said to be covered in the sense of Vitali by a family F of closed sets if each Fe F has positive μ - measure and there is a positive ...
Page 725
... measure . ( Hint . Consider the map f ( s ) → ZA ( s ) f ( ps ) for each A e Σ with μ ( 4 ) < ∞ . ) 37 Let ( S , E , μ ) be a positive measure space , and T a non - nega- tive linear transformation of L1 ( S , E , μ ) into itself ...
... measure . ( Hint . Consider the map f ( s ) → ZA ( s ) f ( ps ) for each A e Σ with μ ( 4 ) < ∞ . ) 37 Let ( S , E , μ ) be a positive measure space , and T a non - nega- tive linear transformation of L1 ( S , E , μ ) into itself ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ