Linear Operators: General theory |
From inside the book
Results 1-3 of 79
Page 412
... linear functional on the vector space X , and let Y be a subspace of X. If f ( Y ) is not the whole field of scalars , then f ( Y ) = 0 . PROOF . Suppose that there exists a ye with f ( y ) 0. Then f ( xy | f ( y ) ) = a , so that every ...
... linear functional on the vector space X , and let Y be a subspace of X. If f ( Y ) is not the whole field of scalars , then f ( Y ) = 0 . PROOF . Suppose that there exists a ye with f ( y ) 0. Then f ( xy | f ( y ) ) = a , so that every ...
Page 417
... linear functional on a linear topological space separates two sets , one of which has an interior point , then the functional is continuous . PROOF . Let X be a linear topological space , and 41 , 4 , CX . Let h be a linear functional ...
... linear functional on a linear topological space separates two sets , one of which has an interior point , then the functional is continuous . PROOF . Let X be a linear topological space , and 41 , 4 , CX . Let h be a linear functional ...
Page 418
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) ‡ ƒ ( q ) . As a last ...
... linear functional separates K and p . 13 COROLLARY . If p and q are distinct points of a locally convex linear topological space X , there is a continuous linear functional f de- fined on such that f ( p ) ‡ ƒ ( q ) . As a last ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ