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 ( a ) = 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 ( a ) = a co ( 4 ) , co ( A + B ) = co ( 4 ) + co ( B ) . If X is a linear topological space , then ...
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 ⇒ CP ⇒ DPD C. The proof of the implication CP⇒ DPk = DC . which is the proof of Lemma 14 is very similar to the proof ...
... 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 ⇒ DPD C. The proof of the implication CP⇒ DPk = DC . which is the proof of Lemma 14 is very similar to the proof ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
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 compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality 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 o-field 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 topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ