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 ) . On the unitary equivalence in general Euclidean space . Proc . Japan Acad . 22 , 242-245 ...
... Proc . Imp . Acad . Tokyo 17 , 121–124 ( 1941 ) . Vector lattices and additive set functions . Proc . Imp . Acad . Tokyo 17 , 228-232 ( 1941 ) . On the unitary equivalence in general Euclidean space . Proc . Japan Acad . 22 , 242-245 ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ