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 { MM2 } and ( 1 - E ) X = N1N2 ; ( c ) if E = EE , then E is a projection with EX = M1M2 and ... projections in B ( VI.3.2 481 PROJECTIONS.
... projection with EX sp { MM2 } and ( 1 - E ) X = N1N2 ; ( c ) if E = EE , then E is a projection with EX = M1M2 and ... 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
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
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 closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ