Linear Operators: General theory |
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Page 479
... satisfies the equation T * y * = 0 . - For operators in a Hilbert space , a slightly different notion of the adjoint is customary . Let be a Hilbert space , and let T ← B ( § ) . Then the adjoint operator T1 of T is in B ...
... satisfies the equation T * y * = 0 . - For operators in a Hilbert space , a slightly different notion of the adjoint is customary . Let be a Hilbert space , and let T ← B ( § ) . Then the adjoint operator T1 of T is in B ...
Page 495
... satisfies properties ( i ) and ( ii ) above so that B ( h ) Bo . This proves that if h e C ( S ) and ƒ e Bo , then fh e Bo . Now let ƒ be a fixed element of Bo , and let B ( f ) = { ge Bofg € Bo } . We have just proved that C ( S ) B ...
... satisfies properties ( i ) and ( ii ) above so that B ( h ) Bo . This proves that if h e C ( S ) and ƒ e Bo , then fh e Bo . Now let ƒ be a fixed element of Bo , and let B ( f ) = { ge Bofg € Bo } . We have just proved that C ( S ) B ...
Page 613
... satisfies the functional equations ƒ ( 0 ) = 1 , f ( t + u ) = f ( t ) f ( u ) . A corresponding problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations ( i ) ...
... satisfies the functional equations ƒ ( 0 ) = 1 , f ( t + u ) = f ( t ) f ( u ) . A corresponding problem is to determine the most general continuous operator valued functions defined on the range t≥0 , which satisfy the equations ( i ) ...
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