Linear Operators: General theory |
From inside the book
Results 1-3 of 81
Page 83
... shown by Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of ...
... shown by Banach [ 7 ] ( see also Banach [ 1 ; Chap . 1 ] and Kuratowski [ 1 ] ) . Conditions of this nature are extended to polynomial operators by Mazur and Orlicz [ 2 ] . It is sometimes useful to define a notion of " continuity " of ...
Page 271
... shown that there exists n1 , . , nr no such that min \ ƒ ( 8n , ) — ƒ ( 80 ) | < ε , je Fo 1≤i≤r which proves the quasi - uniform convergence of ƒ ( s ) to ƒ ( s ) . Thus ( 3 ) implies ( 4 ) . We now show that ( 4 ) implies ( 5 ) ...
... shown that there exists n1 , . , nr no such that min \ ƒ ( 8n , ) — ƒ ( 80 ) | < ε , je Fo 1≤i≤r which proves the quasi - uniform convergence of ƒ ( s ) to ƒ ( s ) . Thus ( 3 ) implies ( 4 ) . We now show that ( 4 ) implies ( 5 ) ...
Page 553
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and coin- cide . This is not the ...
... shown that in Hilbert space C is a maximal two - sided ideal . We have seen in Theorems 7.4 and 8.12 that in the spaces C and L1 , FCCC WCP . Grothendieck [ 4 ; p . 153 ] proved that in C , the ideals W and coin- cide . This is not the ...
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