Linear Operators: General theory |
From inside the book
Results 1-3 of 89
Page 8
... subsets of a set has the property that A € E if and only if every finite subset of A belongs to & , then & contains a maximal element . 3 Derive Theorem 6 from the statement of Exercise 2 . 4 Show that any one of the following implies ...
... subsets of a set has the property that A € E if and only if every finite subset of A belongs to & , then & contains a maximal element . 3 Derive Theorem 6 from the statement of Exercise 2 . 4 Show that any one of the following implies ...
Page 17
... subset of a normal space has a real continuous extension defined on the whole space . PROOF . The only case where the theorem does not apply imme- diately is the case where ƒ is unbounded . If ƒ is real and continuous on the closed set ...
... subset of a normal space has a real continuous extension defined on the whole space . PROOF . The only case where the theorem does not apply imme- diately is the case where ƒ is unbounded . If ƒ is real and continuous on the closed set ...
Page 440
... subset of K which furnishes a lower bound for 1 . It follows by Zorn's lemma that contains a minimal element A. Suppose that A contains two distinct points p and q . Then , by 2.13 , there is a functional ** such that Rx * ( p ) # Rx ...
... subset of K which furnishes a lower bound for 1 . It follows by Zorn's lemma that contains a minimal element A. Suppose that A contains two distinct points p and q . Then , by 2.13 , there is a functional ** such that Rx * ( p ) # Rx ...
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