Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 51
... linear topological space . Then the denumerable set of vectors of the form ax + ... + ẞy with a , Po and x , ... , y ... 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 a , Po and x , ... , y ... 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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
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