Linear Operators: General theory |
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Page 22
... finite number of an Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of 4 , and there- fore most certainly does have a convergent subsequence . This contra ...
... finite number of an Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of 4 , and there- fore most certainly does have a convergent subsequence . This contra ...
Page 200
... finite number of x , μ is non - negative and Ma ( Sa ) 1. In this case the product II ( E ) is meaningful for the αελ type of set P E mentioned above , since ES and hence u ( S ) = 1 αελ α = α α for all but a finite number of a . We ...
... finite number of x , μ is non - negative and Ma ( Sa ) 1. In this case the product II ( E ) is meaningful for the αελ type of set P E mentioned above , since ES and hence u ( S ) = 1 αελ α = α α for all but a finite number of a . We ...
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 - 21 ) ' 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 - 21 ) ' x = 0 } where v is the order of the pole . PROOF . Since σ ( T ) is ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ