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 463
... proved that in the case of a separable space these notions coincide with that of closure in the topology of X * . Alaoglu [ 1 ; p . 256 ] and Kakutani [ 2 ; p . 170 ] independently established the equivalence of these types of closure ...
... proved that in the case of a separable space these notions coincide with that of closure in the topology of X * . Alaoglu [ 1 ; p . 256 ] and Kakutani [ 2 ; p . 170 ] independently established the equivalence of these types of closure ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space 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 Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ