Linear Operators: General theory |
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Page 14
... topological spaces , and if f : XY and g : YZ are continuous , then the ... 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 are ...
... topological spaces , and if f : XY and g : YZ are continuous , then the ... 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 are ...
Page 51
... topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real number & 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 & 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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite 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 TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ