Linear Operators: General theory |
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Page 3
... complex number systems . By the extended real number system we mean the real numbers with the symbols + and -∞ adjoined ; by the extended complex number system we mean the complex numbers with the single symbol ∞ adjoined . If A is a ...
... complex number systems . By the extended real number system we mean the real numbers with the symbols + and -∞ adjoined ; by the extended complex number system we mean the complex numbers with the single symbol ∞ adjoined . If A is a ...
Page 238
... complex valued functions f , g defined on a specified domain S. Here , addition and multiplication are understood to ... numbers when the real and the complex B - spaces under consideration actually require separate treatment . The proof ...
... complex valued functions f , g defined on a specified domain S. Here , addition and multiplication are understood to ... numbers when the real and the complex B - spaces under consideration actually require separate treatment . The proof ...
Page 556
... complex numbers 2 such that 21 - T is not one - to - one . The index v ( 2 ) of a complex number 2 is the smallest non - negative integer v such that ( 1 - T ) = 0 for every vector x for which ( 1 - T ) + 1x = 0 . = It follows that if 2 ...
... complex numbers 2 such that 21 - T is not one - to - one . The index v ( 2 ) of a complex number 2 is the smallest non - negative integer v such that ( 1 - T ) = 0 for every vector x for which ( 1 - T ) + 1x = 0 . = It follows that if 2 ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ