Linear Operators: General theory |
From inside the book
Results 1-3 of 82
Page 183
... follows immediately . Clearly , g ( $ ( · ) ) is a μ - integrable simple function if g is a μ2- integrable simple function . From the definition of μ , it follows that for such a function g we have √ £ 8 ( §2 ) μ2 ( ds2 ) = √2 - 1 ( x ) ...
... follows immediately . Clearly , g ( $ ( · ) ) is a μ - integrable simple function if g is a μ2- integrable simple function . From the definition of μ , it follows that for such a function g we have √ £ 8 ( §2 ) μ2 ( ds2 ) = √2 - 1 ( x ) ...
Page 403
... follows easily from ( 1 ) that ( 2 ) = Mo ( e ) . Equation ( 2 ) enables us to define a Gauss measure in real Hilbert space as follows . Call a Borel subset e of a cylinder set if there exists an orthogonal projection E of 5 onto a ...
... follows easily from ( 1 ) that ( 2 ) = Mo ( e ) . Equation ( 2 ) enables us to define a Gauss measure in real Hilbert space as follows . Call a Borel subset e of a cylinder set if there exists an orthogonal projection E of 5 onto a ...
Page 714
... follows from its definition that Ep is a projection , that EpED = EDEP 0 , and that I = Ep + Ep . Further T commutes ... follows that T " xp → 0 and Tap → 0 ; but since XD { T } has infinitely many terms equal to ap , it follows that ...
... follows from its definition that Ep is a projection , that EpED = EDEP 0 , and that I = Ep + Ep . Further T commutes ... follows that T " xp → 0 and Tap → 0 ; but since XD { T } has infinitely many terms equal to ap , it follows that ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
31 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 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