Linear Operators: General theory |
From inside the book
Results 1-3 of 81
Page 289
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞ . Then the steps in the proof of Theorem 1 apply without change through the point ...
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞ . Then the steps in the proof of Theorem 1 apply without change through the point ...
Page 434
... proof of the preceding theo- rem to construct a subsequence { ym } of { x } such that lim →→ x * ym exists for each x * in the set H of that proof . Let K Co { ym , Ym + 1 , • • • } and let yo be an arbitrary point in Yo ∞ m = 1 m ...
... proof of the preceding theo- rem to construct a subsequence { ym } of { x } such that lim →→ x * ym exists for each x * in the set H of that proof . Let K Co { ym , Ym + 1 , • • • } and let yo be an arbitrary point in Yo ∞ m = 1 m ...
Page 699
... proof of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CP . For technical reasons ... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 → CP DPD ...
... proof of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CP . For technical reasons ... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 → CP DPD ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ