Linear Operators: General theory |
From inside the book
Results 1-3 of 25
Page 124
... sufficiently large k , and we may assume without loss of generality that f ̧h , ( s ) v ( μ , ds ) < 2ɛ for all k . By the simple form of the functions h the set n Ek = { sh ( s ) > y } is in for each y > 0. Moreover , yv ( μ , Ek ) ...
... sufficiently large k , and we may assume without loss of generality that f ̧h , ( s ) v ( μ , ds ) < 2ɛ for all k . By the simple form of the functions h the set n Ek = { sh ( s ) > y } is in for each y > 0. Moreover , yv ( μ , Ek ) ...
Page 592
... sufficiently near 2 , the inverse T - 1 ( 2 ) exists and is an analytic function of λ in a neighborhood of 20. To prove the second part of the lemma we suppose that there is a number 26 in D and a sequence { m } CD such that leo ( T ...
... sufficiently near 2 , the inverse T - 1 ( 2 ) exists and is an analytic function of λ in a neighborhood of 20. To prove the second part of the lemma we suppose that there is a number 26 in D and a sequence { m } CD such that leo ( T ...
Page 637
... sufficiently large t . On the other hand , we have seen that Y is integrable over every finite interval of the positive real axis . Thus , if we choose w1 sufficiently large , • 00 So e - wity ( t ) dt < ∞o . Consequently , by III.6.16 ...
... sufficiently large t . On the other hand , we have seen that Y is integrable over every finite interval of the positive real axis . Thus , if we choose w1 sufficiently large , • 00 So e - wity ( t ) dt < ∞o . Consequently , by III.6.16 ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
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