Linear Operators: General theory |
From inside the book
Results 1-3 of 44
Page 88
... isometric isomorphism of X and X ** under the natural mapping x defined in 3.18 . James [ 4 , 5 ] has proved the following startling theorem . THEOREM . There exists a separable B - space which is isomorphic and isometric with its ...
... isometric isomorphism of X and X ** under the natural mapping x defined in 3.18 . James [ 4 , 5 ] has proved the following startling theorem . THEOREM . There exists a separable B - space which is isomorphic and isometric with its ...
Page 247
... isometric isomorphism of ( 1 % ) * onto l . PROOF . It is clear that the mapping is an isomorphism . To see that it is also an isometric map we suppose first that 1 < p < ∞ . Then , from Minkowski's inequality ( III.3.3 ) , n n │x * x ...
... isometric isomorphism of ( 1 % ) * onto l . PROOF . It is clear that the mapping is an isomorphism . To see that it is also an isometric map we suppose first that 1 < p < ∞ . Then , from Minkowski's inequality ( III.3.3 ) , n n │x * x ...
Page 313
... isometric isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all μ , in ba ( S1 , 1 ) . PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that the ...
... isometric isomorphism of ba ( S1 , E1 ) onto ca ( S1 , E2 ) . ( c ) If E1 is in Σ1 then v ( μ1 , E1 ) = v ( U ( μ1 ) , E1 ) for all μ , in ba ( S1 , 1 ) . PROOF . Recalling that is an isomorphism of Σ onto 1 , it is clear that 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