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 -∞o 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 -∞o 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 & such that λI - T is not one - to - one . The index v ( 2 ) of a complex number is the smallest non - negative integer v such that ( 21 - T ) = 0 for every vector x for which ( 1 - T ) + 1x 0 . = - = It follows that if ...
... complex numbers & such that λI - T is not one - to - one . The index v ( 2 ) of a complex number is the smallest non - negative integer v such that ( 21 - T ) = 0 for every vector x for which ( 1 - T ) + 1x 0 . = - = It follows that if ...
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