Linear Operators: General theory |
From inside the book
Results 1-3 of 83
Page 2
... disjoint family if every pair of distinct sets in the family is disjoint . A sequence { a , } of sets is a sequence of disjoint sets if an for nm . A set a is said to intersect a set b if ab ‡ 4 . The terms function , mapping ...
... disjoint family if every pair of distinct sets in the family is disjoint . A sequence { a , } of sets is a sequence of disjoint sets if an for nm . A set a is said to intersect a set b if ab ‡ 4 . The terms function , mapping ...
Page 15
... disjoint neighborhoods of x and y . ( c ) For every closed set A , and every ≈ & A , there are disjoint neighborhoods of A and x . ( d ) For every pair of disjoint closed sets A and B , there are dis- joint neighborhoods of A and B. 2 ...
... disjoint neighborhoods of x and y . ( c ) For every closed set A , and every ≈ & A , there are disjoint neighborhoods of A and x . ( d ) For every pair of disjoint closed sets A and B , there are dis- joint neighborhoods of A and B. 2 ...
Page 320
... disjoint sets in Σ . A number of elementary properties of the semi - variation are listed in the next lemma . 4 LEMMA . Let u be a vector valued measure . Then ( a ) || u || ( E ) ≥ μ ( E ) | ≥ 0 , ΕΕΣ ; ( b ) || μ || ( E ) ≤ 4 sup ...
... disjoint sets in Σ . A number of elementary properties of the semi - variation are listed in the next lemma . 4 LEMMA . Let u be a vector valued measure . Then ( a ) || u || ( E ) ≥ μ ( E ) | ≥ 0 , ΕΕΣ ; ( b ) || μ || ( E ) ≤ 4 sup ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ