Linear Operators: General theory |
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Page 3
... real function defined by the equations Xɛ ( s ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Ε = Sometimes , when the ... numbers with the symbols + and -∞o adjoined ; by the extended complex number system we mean the complex numbers with the ...
... real function defined by the equations Xɛ ( s ) = 1 , se E , and Xɛ ( s ) = 0 , s ¢ E. Ε = Sometimes , when the ... numbers with the symbols + and -∞o adjoined ; by the extended complex number system we mean the complex numbers with the ...
Page 4
... real numbers , it is conventional to take sup , infp . 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 de ...
... real numbers , it is conventional to take sup , infp . 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 de ...
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 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ