Linear Operators: General theory |
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Page 733
... Trans . Amer . Math . Soc . 61 , 106-121 ( 1947 ) . Direct sum theorem for Haar measures . Trans . Amer . Math . Soc . 61 , 122-127 ( 1947 ) . 4. Spectral resolution of groups of unitary operators . Duke Math . J. 11 , 589-595 ( 1944 ) ...
... Trans . Amer . Math . Soc . 61 , 106-121 ( 1947 ) . Direct sum theorem for Haar measures . Trans . Amer . Math . Soc . 61 , 122-127 ( 1947 ) . 4. Spectral resolution of groups of unitary operators . Duke Math . J. 11 , 589-595 ( 1944 ) ...
Page 790
... Trans . Amer . Math . Soc . 37 , 301-338 ( 1935 ) . Linear transformations in L ,, p > 1. Trans . Amer . Math . Soc . 39 , 83-100 ( 1936 ) . 6. Bilinear transformations in Hilbert space . Trans . Amer . Math . Soc . 45 , 474-507 ( 1939 ) ...
... Trans . Amer . Math . Soc . 37 , 301-338 ( 1935 ) . Linear transformations in L ,, p > 1. Trans . Amer . Math . Soc . 39 , 83-100 ( 1936 ) . 6. Bilinear transformations in Hilbert space . Trans . Amer . Math . Soc . 45 , 474-507 ( 1939 ) ...
Page 797
... Trans . Amer . Math . Soc . 44 , 277-304 ( 1938 ) . 5. On continuity and openness of homomorphisms in topological ... Trans . Amer . Math . Soc . 48 , 516-541 ( 1940 ) . A note on ergodic theory . Proc . Amer . Math . Soc . 2 , 662–669 ...
... Trans . Amer . Math . Soc . 44 , 277-304 ( 1938 ) . 5. On continuity and openness of homomorphisms in topological ... Trans . Amer . Math . Soc . 48 , 516-541 ( 1940 ) . A note on ergodic theory . Proc . Amer . Math . Soc . 2 , 662–669 ...
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