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 ( a4 ) = 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 ( a4 ) = 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 { y } of { x } such that limx x * Ym exists for each a * in the set H of that proof . Let Km co yms ym + 1 } and let yo be an arbitrary point in K. For each a * X * , we have x ...
... proof of the preceding theo- rem to construct a subsequence { y } of { x } such that limx x * Ym exists for each a * in the set H of that proof . Let Km co yms ym + 1 } and let yo be an arbitrary point in K. For each a * X * , we have x ...
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 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