Linear Operators: General theory |
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Page 373
... proved for closed linear manifolds in L2 [ 0 , 1 ] by E. Fischer [ 2 ] . The fact that a linear manifold which is not dense in the entire space has a non - zero orthogonal complement ( proved in 4.4 ) was proved without the assumption ...
... proved for closed linear manifolds in L2 [ 0 , 1 ] by E. Fischer [ 2 ] . The fact that a linear manifold which is not dense in the entire space has a non - zero orthogonal complement ( proved in 4.4 ) was proved without the assumption ...
Page 385
... proved independently by Cech [ 1 ] only slightly later . ( See also Stone [ 5 ] for an elementary treatment . ) Lemma 6.25 was proved in Stone [ 1 ; p . 465 ] -extensions of this re- sult are also found in Hewitt [ 5 ] and Kaplansky ...
... proved independently by Cech [ 1 ] only slightly later . ( See also Stone [ 5 ] for an elementary treatment . ) Lemma 6.25 was proved in Stone [ 1 ; p . 465 ] -extensions of this re- sult are also found in Hewitt [ 5 ] and Kaplansky ...
Page 462
... proved 3.9 after establishing Lemma 3.10 by induction . The case of Theorem 3.9 in which X = Y * and à * and I , was proved in the separa- ble case by Banach [ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p . 256 ] . Michael ...
... proved 3.9 after establishing Lemma 3.10 by induction . The case of Theorem 3.9 in which X = Y * and à * and I , was proved in the separa- ble case by Banach [ 1 ; p . 131 ] and in full generality by Alaoglu [ 1 ; p . 256 ] . Michael ...
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