Linear Operators: General theory |
From inside the book
Results 1-3 of 93
Page 51
... linear topological space . Then the denumerable set of vectors of the form ax + ... + ẞy with α , Po and x , y in B ... linear topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real ...
... linear topological space . Then the denumerable set of vectors of the form ax + ... + ẞy with α , Po and x , y in B ... linear topological space X is bounded if , given any neighborhood V of the zero in X , there exists a positive real ...
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 linear ...
... 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 linear ...
Page 436
... linear vector space . Show that X is a total space of linear functionals on X. 2 If is an infinite dimensional B - space then X * X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if and ...
... linear vector space . Show that X is a total space of linear functionals on X. 2 If is an infinite dimensional B - space then X * X * . 3 Let X be a linear topological space . Then X has a non - zero continuous linear functional if and ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
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