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Page 481
... projection with EX sp { MM2 } and ( I - E ) X = N1 ^ N2 ; ( c ) if E = EE2 , then E is a projection with EX = ( 1 ... projections in B ( VI.3.2 481 PROJECTIONS.
... projection with EX sp { MM2 } and ( I - E ) X = N1 ^ N2 ; ( c ) if E = EE2 , then E is a projection with EX = ( 1 ... 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 , ( I - E ) , the above iden- E§ 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 , ( I - E ) , the above iden- E§ tity shows that there is a one - to ...
Page 514
... projection with n dimensional range . 20 A projection has finite dimensional range if and only if it is compact . 21 A linear mapping E such that E2 = E is a projection ( i.e. , is bounded ) if and only if the ranges of E and I - E are ...
... projection with n dimensional range . 20 A projection has finite dimensional range if and only if it is compact . 21 A linear mapping E such that E2 = E is a projection ( i.e. , is bounded ) if and only if the ranges of E and I - E are ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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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