Linear Operators: General theory |
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Page 261
... mean that f ( s ) g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining a * y * to mean that x * f ≥y * f for every f € C ( S ) with f 0 . Before representing the conjugate space C * ( S ) we first observe that ...
... mean that f ( s ) g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining a * y * to mean that x * f ≥y * f for every f € C ( S ) with f 0 . Before representing the conjugate space C * ( S ) we first observe that ...
Page 660
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages { N - 1 NT " } converges in the uniform topology of operators . Finally ...
... mean and pointwise convergence theorems for the contin- uous case . Section 8 is concerned with a certain class of operators T for which the sequence of averages { N - 1 NT " } converges in the uniform topology of operators . Finally ...
Page 724
... mean of L1 ( S , Σ , m ) for every fe L1 ( S , Z , m ) only if there exists a constant K < ∞ such that 1 n - 1 n Σm ( p - ie ) ≤ Km ( e ) , i = 0 = 0 n = 0 , 1 , . . .. 34 ( Y. N. Dowker ) Let S , Z , q , m be as in Exercise 31. Show ...
... mean of L1 ( S , Σ , m ) for every fe L1 ( S , Z , m ) only if there exists a constant K < ∞ such that 1 n - 1 n Σm ( p - ie ) ≤ Km ( e ) , i = 0 = 0 n = 0 , 1 , . . .. 34 ( Y. N. Dowker ) Let S , Z , q , m be as in Exercise 31. Show ...
Contents
Preliminary Concepts | 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 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