Linear Operators: General theory |
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Page 415
... proof , the same result holds for non - Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co ( x4 ) = a co ( 4 ) , co ( A + B ) = co ( 4 ) + co ( B ) . If X is a linear topological space , then ...
... proof , the same result holds for non - Abelian topological groups . 4 LEMMA . For arbitrary sets A , B in a linear space X : ( i ) co ( x4 ) = a co ( 4 ) , co ( A + B ) = co ( 4 ) + co ( B ) . If X is a linear topological space , then ...
Page 434
... proof of the preceding theo- rem to construct a subsequence { m } of { x } such that lim , x x * Ym exists for each a * in the set H of that proof . Let Km co { ym , Ym + 1 , · · . } and let yo be an arbitrary point in 00 m = 1 = K. For ...
... proof of the preceding theo- rem to construct a subsequence { m } of { x } such that lim , x x * Ym exists for each a * in the set H of that proof . Let Km co { ym , Ym + 1 , · · . } and let yo be an arbitrary point in 00 m = 1 = K. For ...
Page 699
... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 = CPK ⇒ DP⇒ Dž⇒ Ck . The proof of the implication CP1⁄2 ⇒ DP1⁄2 which is the proof of Lemma 14 is very similar to the ...
... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 = CPK ⇒ DP⇒ Dž⇒ Ck . The proof of the implication CP1⁄2 ⇒ DP1⁄2 which is the proof of Lemma 14 is very similar to the ...
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