Linear Operators: General theory |
From inside the book
Results 1-3 of 92
Page 20
... complete metric space is com- plete . A complete subspace of a metric space is closed . 8 LEMMA . A mapping f : X → Y between metric spaces is contin- uous at the point x if and only if { f ( x ) } converges to f ( x ) , whenever { x } ...
... complete metric space is com- plete . A complete subspace of a metric space is closed . 8 LEMMA . A mapping f : X → Y between metric spaces is contin- uous at the point x if and only if { f ( x ) } converges to f ( x ) , whenever { x } ...
Page 311
... complete . If S is a topological space , the rba ( S ) is also weakly complete . PROOF . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such that B ( S , E ) ...
... complete . If S is a topological space , the rba ( S ) is also weakly complete . PROOF . Consider the closed subspace B ( S , E ) of B ( S ) . According to Theorems 6.18 and 6.20 there is a compact Hausdorff space S1 such that B ( S , E ) ...
Page 840
... Complete and o - complete lattice , ( 43 ) Complete metric space , compact , 1.6.15 ( 22 ) definition , I.6.5 ( 19 ) properties , 1.6.7 ( 20 ) , I.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in ...
... Complete and o - complete lattice , ( 43 ) Complete metric space , compact , 1.6.15 ( 22 ) definition , I.6.5 ( 19 ) properties , 1.6.7 ( 20 ) , I.6.9 ( 20 ) Complete normed linear space . ( See B - space ) Complete orthonormal set , in ...
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