Linear Operators: General theory |
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Page 289
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞ . Then the steps in the proof of Theorem 1 apply without change through the point ...
... PROOF . This follows from Corollary 2 and Theorem II.3.28 . Q.E.D. Next we consider the problem of representing the ... PROOF . First assume μ ( S ) < ∞ . Then the steps in the proof of Theorem 1 apply without change through the point ...
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 699
... proof of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CPk . For technical reasons ... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 = CP DP ...
... proof of the lemma . Q.E.D. We shall now state and prove the lemma referred to as CPk . For technical reasons ... proof of this lemma is the most involved of all the steps in the proof of Lemma 11 as outlined in the diagram : C1 = CP DP ...
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