Linear Operators: General theory |
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Page 181
... preceding argument . Thus only formula [ * ] remains to be verified . By the argument used in the proof of Corollary 5 it is seen that it will be sufficient to prove [ * ] in the case when g is a positive real function . It is also ...
... preceding argument . Thus only formula [ * ] remains to be verified . By the argument used in the proof of Corollary 5 it is seen that it will be sufficient to prove [ * ] in the case when g is a positive real function . It is also ...
Page 290
... preceding theorem remains valid if S is the union of a ( possibly uncountable ) collection of disjoint subsets { S } in each of which is o - finite and such that if E e Σ and μ ( E ) < ∞ , then E has non - void intersection with at ...
... preceding theorem remains valid if S is the union of a ( possibly uncountable ) collection of disjoint subsets { S } in each of which is o - finite and such that if E e Σ and μ ( E ) < ∞ , then E has non - void intersection with at ...
Page 396
... preceding paragraph we have discussed the characterization of the space L1 as a concrete represen- tation of the abstract L - spaces . Bohnenblust [ 1 ] has given a very interesting characterization of the L , spaces , 1 ≤ p < ∞o . We ...
... preceding paragraph we have discussed the characterization of the space L1 as a concrete represen- tation of the abstract L - spaces . Bohnenblust [ 1 ] has given a very interesting characterization of the L , spaces , 1 ≤ p < ∞o . We ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ