Linear Operators: General theory |
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Page 2
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B but not in 4 , i.e. , the set { xx e B , xe A } . This set is sometimes denoted by B - A . In a discussion where the ...
... mean that A is a proper subset of B. The complement of a set A relative to a set B is the set whose elements are in B but not in 4 , i.e. , the set { xx e B , xe A } . This set is sometimes denoted by B - A . In a discussion where the ...
Page 261
... mean that f ( s ) ≥ g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining * y * to mean that x * f ≥ y * f for every ƒ € C ( S ) with f≥ 0 . Before representing the conjugate space C * ( S ) we first observe ...
... mean that f ( s ) ≥ g ( s ) for all s in S. Finally , C * ( S ) is partially ordered by defining * y * to mean that x * f ≥ y * f for every ƒ € C ( S ) with f≥ 0 . Before representing the conjugate space C * ( S ) we first observe ...
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 - T " } converges in the EXT uniform topology of operators ...
... 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 - T " } converges in the EXT uniform topology of operators ...
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