Linear Operators: General theory |
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Page 770
... Proc . Second Berkeley Symposium Math . Statistics and Prob . , 189-215 ( 1951 ) . Kaczmarz , S. , and Steinhaus , H ... Proc . Imp . Acad . Tokyo 13 , 93-94 ( 1937 ) . 2 . 3 . 4 . Weak topology and regularity of Banach spaces . Proc ...
... Proc . Second Berkeley Symposium Math . Statistics and Prob . , 189-215 ( 1951 ) . Kaczmarz , S. , and Steinhaus , H ... Proc . Imp . Acad . Tokyo 13 , 93-94 ( 1937 ) . 2 . 3 . 4 . Weak topology and regularity of Banach spaces . Proc ...
Page 821
... Proc . XII Scand . Math . Congress , Lund ( 1953 ) . 3. Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4 . 5 . 6 . 7 . 8 . On invariant subspaces of normal operators . Proc . Amer . Math . Soc ...
... Proc . XII Scand . Math . Congress , Lund ( 1953 ) . 3. Commuting spectral measures on Hilbert space . Pacific J. Math . 4 , 355–361 ( 1954 ) . 4 . 5 . 6 . 7 . 8 . On invariant subspaces of normal operators . Proc . Amer . Math . Soc ...
Page 825
... Proc . Imp . Acad . Tokyo 17 , 121–124 ( 1941 ) . Vector lattices and additive set functions . Proc . Imp . Acad . Tokyo 17 , 228-232 ( 1941 ) . 2 . 3 . 4 . On the unitary equivalence in general Euclidean space . Proc . Japan Acad . 22 ...
... Proc . Imp . Acad . Tokyo 17 , 121–124 ( 1941 ) . Vector lattices and additive set functions . Proc . Imp . Acad . Tokyo 17 , 228-232 ( 1941 ) . 2 . 3 . 4 . On the unitary equivalence in general Euclidean space . Proc . Japan Acad . 22 ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian 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