Linear Operators: General theory |
From inside the book
Results 1-3 of 51
Page 119
... consider a function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set ... considering this somewhat more extended class of functions we make no change in F ( S , Z , μ , X ) , or in any of ...
... consider a function ƒ ( vector or extended real - valued ) which is defined only on the complement of a u - null set ... considering this somewhat more extended class of functions we make no change in F ( S , Z , μ , X ) , or in any of ...
Page 335
... Consider the family W of subsets of 4 , which are well - ordered under the ordering inherited from L. We shall order W by defining the rela- tion a≤ b between elements a , b in W to mean that a Cb and that each element x which is in b ...
... Consider the family W of subsets of 4 , which are well - ordered under the ordering inherited from L. We shall order W by defining the rela- tion a≤ b between elements a , b in W to mean that a Cb and that each element x which is in b ...
Page 468
... consider real Euclidean space . Further , the Weierstrass approximation theorem for continuous functions of n variables implies that every continuous map of S into itself is the uniform limit of a sequence { } of infinite- ly ...
... consider real Euclidean space . Further , the Weierstrass approximation theorem for continuous functions of n variables implies that every continuous map of S into itself is the uniform limit of a sequence { } of infinite- ly ...
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