Linear Operators: General theory |
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Page 14
... topological spaces , and if f : X → Y and g : Y → Z are continuous , then ... space X , and let a be a scalar . Then the functions given by the ... topological space , a continuous real function . which is not a constant ? If x and y ...
... topological spaces , and if f : X → Y and g : Y → Z are continuous , then ... space X , and let a be a scalar . Then the functions given by the ... topological space , a continuous real function . which is not a constant ? If x and y ...
Page 51
... topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number ɛ such that BC V providing a ≤ ε . 8 LEMMA . A compact subset of a linear topological space is bounded . PROOF . Let B ...
... topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number ɛ such that BC V providing a ≤ ε . 8 LEMMA . A compact subset of a linear topological space is bounded . PROOF . Let B ...
Page 419
... topology of X. The following lemma is a consequence of Definition 2 . 3 LEMMA . If I is a total linear space of linear functionals on X , X is a locally convex linear topological space in its П topology . Note that may already be a ...
... topology of X. The following lemma is a consequence of Definition 2 . 3 LEMMA . If I is a total linear space of linear functionals on X , X is a locally convex linear topological space in its П topology . Note that may already be a ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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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