Linear Operators: General theory |
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Page 3
... real function defined by the equations XE ( S ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Sometimes , when the range of ... numbers with the symbols + and -∞o adjoined ; by the extended complex number system we mean the complex numbers ...
... real function defined by the equations XE ( S ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Sometimes , when the range of ... numbers with the symbols + and -∞o adjoined ; by the extended complex number system we mean the complex numbers ...
Page 4
... real numbers , it is conventional to take sup , + ∞ info . If A is an infinite set of real numbers , then the symbol lim sup A denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the ...
... real numbers , it is conventional to take sup , + ∞ info . If A is an infinite set of real numbers , then the symbol lim sup A denotes the infimum of all numbers b with the property that only a finite set of numbers in A exceed b ; the ...
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
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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 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