Linear Operators: General theory |
From inside the book
Results 1-3 of 90
Page 14
... topological spaces , and if f : X → Y and g : Y Z 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 : X → Y and g : Y Z 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 BCV 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 BCV 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 I 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 I topology . Note that may already be a ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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