Linear Operators: General theory |
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Page 412
... linear functional on the vector space X , and let be a subspace of X. If f ( 9 ) is not the whole field of scalars , then f ( 9 ) = 0 . = PROOF . Suppose that there exists a ye f ( ay / f ( y ) ) = a , so that every scalar is in f ( Y ) ...
... linear functional on the vector space X , and let be a subspace of X. If f ( 9 ) is not the whole field of scalars , then f ( 9 ) = 0 . = PROOF . Suppose that there exists a ye f ( ay / f ( y ) ) = a , so that every scalar is in f ( Y ) ...
Page 418
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) f ( q ) . As a last corollary ...
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) f ( q ) . As a last corollary ...
Page 452
... linear topological space X , and K ‡ X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and Ρ is in A , then there exists a non - zero continuous linear functional tangent to A at ...
... linear topological space X , and K ‡ X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and Ρ is in A , then there exists a non - zero continuous linear functional tangent to A at ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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