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 ) CHOM , 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 ) CHOM , we see that E ...
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 ...
Page 515
... projection , show that its matrix representation is ( a , j ) = ( Σk - Pik Pik ) , where g .. , r is any orthonormal ... projection in Euclidean space , show that tr ( E ) = dim ( M ) . 29 Let E , ... , E , be projections in a finite ...
... projection , show that its matrix representation is ( a , j ) = ( Σk - Pik Pik ) , where g .. , r is any orthonormal ... projection in Euclidean space , show that tr ( E ) = dim ( M ) . 29 Let E , ... , E , be projections in a finite ...
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 B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ