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 ( A ) , 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 ( A ) , 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
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ