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 440
... subset of K which furnishes a lower bound for A1 . It follows by Zorn's lemma that contains a minimal element 4o . Suppose that A contains two distinct points p and q . Then , by 2.13 , there is a functional a * X * such that x * ( p ) ...
... subset of K which furnishes a lower bound for A1 . It follows by Zorn's lemma that contains a minimal element 4o . Suppose that A contains two distinct points p and q . Then , by 2.13 , there is a functional a * X * such that x * ( p ) ...
Page 456
... subset of a locally convex linear topological space has the fixed point property . PROOF . By Zorn's lemma there exists a minimal convex subset K1 of K with the property that TK , C K1 . By the previous lemma , this minimal subset ...
... subset of a locally convex linear topological space has the fixed point property . PROOF . By Zorn's lemma there exists a minimal convex subset K1 of K with the property that TK , C K1 . By the previous lemma , this minimal subset ...
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