Linear Operators: General theory |
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Page 3
... real function defined by the equations % ( s ) = 1 , se E , and ZE ( S ) = 0 , s ¢ E. = Sometimes , when the range of a transformation f : A → B is to be emphasized at the expense of ... real numbers , I.1 3 NOTATION AND ELEMENTARY NOTIONS.
... real function defined by the equations % ( s ) = 1 , se E , and ZE ( S ) = 0 , s ¢ E. = Sometimes , when the range of a transformation f : A → B is to be emphasized at the expense of ... real numbers , I.1 3 NOTATION AND ELEMENTARY NOTIONS.
Page 4
... real numbers , then the symbol lim sup 4 denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of the symbol lim inf A is similar . In particular , if A is a sequence ...
... real numbers , then the symbol lim sup 4 denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the de- finition of the symbol lim inf A is similar . In particular , if A is a sequence ...
Page 11
... real numbers . Another base for this topology is obtained by taking a and b to be rational numbers . A subbase for this topology is given by all infinite intervals ( − ∞ , a ) , ( b , + ∞ ) , where a and b are either real or rational ...
... real numbers . Another base for this topology is obtained by taking a and b to be rational numbers . A subbase for this topology is given by all infinite intervals ( − ∞ , a ) , ( b , + ∞ ) , where a and b are either real or rational ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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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