Linear Operators: General theory |
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Page 251
... projection , i.e. , E2 E , and that E is an orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with DSM then ED = D and , since ( I - D ) CH M , we see that E ...
... projection , i.e. , E2 E , and that E is an orthogonal projection . It is the uniquely determined orthogonal projection with ES = M. For if D is an orthogonal projection with DSM then ED = D and , since ( I - D ) CH M , we see that E ...
Page 481
... projection with EX = sp { M1UM2 } and ( I - E ) X = N1 ^ N2 ; = ( c ) if E EE2 , then E is a projection with EX = M1 ... projections in B ( VI.3.2 481 PROJECTIONS.
... projection with EX = sp { M1UM2 } and ( I - E ) X = N1 ^ N2 ; = ( c ) if E EE2 , then E is a projection with EX = M1 ... projections in B ( VI.3.2 481 PROJECTIONS.
Page 482
... projection is sometimes called an orthogonal or perpendicular projection . Since closed complementary manifolds X and Y determine uniquely a projection E with ES = X , ( 1 - E ) , the above iden- tity shows that there is a one - to ...
... projection is sometimes called an orthogonal or perpendicular projection . Since closed complementary manifolds X and Y determine uniquely a projection E with ES = X , ( 1 - E ) , the above iden- tity shows that there is a one - to ...
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