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Page 272
... fact that ( 5 ) implies ( 1 ) is due to Eberlein and is proved in Chapter V ( cf. V.6.1 ) . Q.E.D. Remark . It should be observed that we can require that the points S1 , S2 , ... in condition ( 4 ) be contained in a preassigned dense ...
... fact that ( 5 ) implies ( 1 ) is due to Eberlein and is proved in Chapter V ( cf. V.6.1 ) . Q.E.D. Remark . It should be observed that we can require that the points S1 , S2 , ... in condition ( 4 ) be contained in a preassigned dense ...
Page 373
... 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 of separability by F. Riesz [ 8 ] . His proof follows the lines of an argument ...
... 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 of separability by F. Riesz [ 8 ] . His proof follows the lines of an argument ...
Page 386
... fact that C [ 0 , 1 ] may be mapped in a linear and homeomorphic manner on the space . C ( [ 0 , 1 ] U 2 ) . ( See Banach [ 1 ; p . 184 ] ) . Weak compactness in B ( S ) . Definition 6.27 is equivalent to a de- finition given by Bartle ...
... fact that C [ 0 , 1 ] may be mapped in a linear and homeomorphic manner on the space . C ( [ 0 , 1 ] U 2 ) . ( See Banach [ 1 ; p . 184 ] ) . Weak compactness in B ( S ) . Definition 6.27 is equivalent to a de- finition given by Bartle ...
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