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Page 96
... symmetric difference ( A - B ) ( B - A ) . 3 DEFINITION . Let S be a set . A field of subsets of S , or a Boolean algebra of subsets of S , is a non - empty family of subsets of S which contains the null set , the complement ( relative ...
... symmetric difference ( A - B ) ( B - A ) . 3 DEFINITION . Let S be a set . A field of subsets of S , or a Boolean algebra of subsets of S , is a non - empty family of subsets of S which contains the null set , the complement ( relative ...
Page 734
... symmetric operators . Proceedings of the Symposium on Spectral Theory and Differen- tial Problems , 179-202 ( 1951 ) . Oklahoma Agricultural and Mechanical College , Stillwater , Oklahoma . 4 . 5 . The Rayleigh - Ritz and A. Weinstein ...
... symmetric operators . Proceedings of the Symposium on Spectral Theory and Differen- tial Problems , 179-202 ( 1951 ) . Oklahoma Agricultural and Mechanical College , Stillwater , Oklahoma . 4 . 5 . The Rayleigh - Ritz and A. Weinstein ...
Page 794
... symmetric operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . 8. Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) ...
... symmetric operator . Izvestiya Akad . Nauk SSSR 4 , 53–104 ( 1940 ) . ( Russian . English summary ) Math . Rev. 2 , 104 ( 1941 ) . 8. Spectral functions of a symmetric operator . Izvestiya Akad . Nauk SSSR ( N. S. ) 4 , 277-318 ( 1940 ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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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