Linear Operators: General theory |
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Page 319
... follows from Theorem II.3.6 that lim y · m - ∞ * nxx exists for every x e X1 , and , in particular , lim yu ( E ) exists for each m m ɛ , m - ∞ E e 21. By Corollary III.7.4 , the set { y } of scalar valued measures is uniformly ...
... follows from Theorem II.3.6 that lim y · m - ∞ * nxx exists for every x e X1 , and , in particular , lim yu ( E ) exists for each m m ɛ , m - ∞ E e 21. By Corollary III.7.4 , the set { y } of scalar valued measures is uniformly ...
Page 557
... PROOF . This follows from Theorem 3. We have seen that T always satisfies a non - zero polynomial equation P ( T ) = 0 , where the roots of P ( 2 ) are the spectral points of T. Q.E.D. Theorem 3 enables us to define the operator f ( T ) ...
... PROOF . This follows from Theorem 3. We have seen that T always satisfies a non - zero polynomial equation P ( T ) = 0 , where the roots of P ( 2 ) are the spectral points of T. Q.E.D. Theorem 3 enables us to define the operator f ( T ) ...
Page 576
Nelson Dunford, Jacob T. Schwartz. PROOF . It follows from Theorem 10 that the map o → E ( σ ) is a homeomorphism . To verify that it is an isomorphism , it will suffice to show that E ( σ ) = 0 only when σ is the void set 4. Now if E ...
Nelson Dunford, Jacob T. Schwartz. PROOF . It follows from Theorem 10 that the map o → E ( σ ) is a homeomorphism . To verify that it is an isomorphism , it will suffice to show that E ( σ ) = 0 only when σ is the void set 4. Now if E ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ