Linear Operators: General theory |
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Page 22
... finite number of a Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A , and there- fore most certainly does have a convergent subsequence . This contra ...
... finite number of a Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A , and there- fore most certainly does have a convergent subsequence . This contra ...
Page 200
... finite number of x , μa is non - negative and μa ( Sa ) = 1. In this case the product II ( E ) is meaningful for the αελ type of set P E mentioned above , since E = S and hence μ ( S ) = 1 αελ α = α α for all but a finite number of a ...
... finite number of x , μa is non - negative and μa ( Sa ) = 1. In this case the product II ( E ) is meaningful for the αελ type of set P E mentioned above , since E = S and hence μ ( S ) = 1 αελ α = α α for all but a finite number of a ...
Page 579
... finite positive index . For such a number 2 , the projection E ( 2 ) has a non - zero finite dimensional range given by the formula E ( 2 ) X = { x | ( T — ¿ I ) x = 0 } where v is the order of the pole . PROOF . Since σ ( T ) is ...
... finite positive index . For such a number 2 , the projection E ( 2 ) has a non - zero finite dimensional range given by the formula E ( 2 ) X = { x | ( T — ¿ I ) x = 0 } where v is the order of the pole . PROOF . Since σ ( T ) is ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ