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 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 disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ