Linear Operators: General theory |
From inside the book
Results 1-3 of 85
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 be a linear topological space , and 41 , 42 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 be a linear topological space , and 41 , 42 CX . Let h be a linear functional ...
Page 452
... linear topological space X , and K X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and P is in A , then there exists a non - zero continuous linear functional tangent to A at p ...
... linear topological space X , and K X , then there exists a non- zero continuous linear functional tangent to K at p . If A is a subset of X , and P is in A , then there exists a non - zero continuous linear functional tangent to A at p ...
Page 454
... continuous , TN : C → K is continuous and by the preceding lemma has a fixed point . This fixed point is in K ; it is therefore a fixed point of the mapping T. Q.E.D. 4 LEMMA . Let K be a compact convex subset of a locally convex linear ...
... continuous , TN : C → K is continuous and by the preceding lemma has a fixed point . This fixed point is in K ; it is therefore a fixed point of the mapping T. Q.E.D. 4 LEMMA . Let K be a compact convex subset of a locally convex linear ...
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