Linear Operators: General theory |
From inside the book
Results 1-3 of 50
Page 481
... projections are summarized in the following lemmas . Further properties will be found in the exer- cises . 2 LEMMA . Let E , and E2 be commuting projections in a B - space X. If M1 = EX , N ... projections in B ( VI.3.2 481 PROJECTIONS.
... projections are summarized in the following lemmas . Further properties will be found in the exer- cises . 2 LEMMA . Let E , and E2 be commuting projections in a B - space X. If M1 = EX , N ... projections in B ( VI.3.2 481 PROJECTIONS.
Page 482
... projections in a B - space . We conclude this section with a few remarks on projections in Hilbert space . Let E be a projection in Hilbert space § , and let E * be its Hilbert space adjoint . Then the identity ( Ex , ( I — E ) y ) ...
... projections in a B - space . We conclude this section with a few remarks on projections in Hilbert space . Let E be a projection in Hilbert space § , and let E * be its Hilbert space adjoint . Then the identity ( Ex , ( I — E ) y ) ...
Page 514
... projections in Hilbert space , then E1E2 = 0 if and only if EE1 = 0 . ( iii ) If E , ... , E , are projections , then E = E1 + ... + E , is a projection if E¿E , 0 for ij . In this case M = M1 ↔ → Mn and N = N1 ... Nn . = ... ( iv ) ...
... projections in Hilbert space , then E1E2 = 0 if and only if EE1 = 0 . ( iii ) If E , ... , E , are projections , then E = E1 + ... + E , is a projection if E¿E , 0 for ij . In this case M = M1 ↔ → Mn and N = N1 ... Nn . = ... ( iv ) ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
80 other sections not shown
Other editions - View all
Common terms and phrases
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