Linear Operators: General theory |
From inside the book
Results 1-3 of 87
Page 126
... valued , complex valued , or extended real valued additive set function defined on a field Σ of subsets of a set S. Then u is said to be countably additive if 00 μ ( UE ) = i = 1 00 i = 1 ( E ) whenever E1 , E2 , . . . are disjoint sets ...
... valued , complex valued , or extended real valued additive set function defined on a field Σ of subsets of a set S. Then u is said to be countably additive if 00 μ ( UE ) = i = 1 00 i = 1 ( E ) whenever E1 , E2 , . . . are disjoint sets ...
Page 224
... valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions which will be used later ...
... valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and this theory will be applied here to obtain the extensions which will be used later ...
Page 238
... complex valued functions f , g defined on a specified domain S. Here , addition and multiplication are understood to ... valued functions with the stated properties , or of all complex valued functions with these properties . Unless the ...
... complex valued functions f , g defined on a specified domain S. Here , addition and multiplication are understood to ... valued functions with the stated properties , or of all complex valued functions with these properties . Unless the ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
59 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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ