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 DH = M then ED = D and , since ( I – D ) CH → M , we see ...
... 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 DH = M then ED = D and , since ( I – D ) CH → M , we see ...
Page 481
... projection with EX sp { M1M2 } and ( I — Е ) X = N1 ^ N2 ; - ( c ) if E = EE2 , then E is a projection with EX ... projections in B ( VI.3.2 481 PROJECTIONS.
... projection with EX sp { M1M2 } and ( I — Е ) X = N1 ^ N2 ; - ( c ) if E = EE2 , then E is a projection with EX ... 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 E§ = X , ( I — E ) H = Y , the above iden- tity shows that there is a one ...
... projection is sometimes called an orthogonal or perpendicular projection . Since closed complementary manifolds X and Y determine uniquely a projection E with E§ = X , ( I — E ) H = Y , the above iden- tity shows that there is a one ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space 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 exists f₁ finite dimensional function defined function f g₁ 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-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ