Linear Operators: General theory |
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Page 177
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { sse F , f ( s ) ≤n } . Then F = UF , and v ( 2 , F ...
Nelson Dunford, Jacob T. Schwartz. may be assumed that λ is real valued . A real valued set function can be represented as the ... assumed to be positive and measurable we can put F { sse F , f ( s ) ≤n } . Then F = UF , and v ( 2 , F ...
Page 278
... assumed that x * = x * f . Then there is a point s in S such that x * f = f ( s ) , fe C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to a ...
... assumed that x * = x * f . Then there is a point s in S such that x * f = f ( s ) , fe C ( S ) . PROOF . By the preceding lemma a * is a point in the space S1 de- fined in the proof of Theorem 18. By Theorem 22 , S is homeomorphic to a ...
Page 657
... assumed to be governed by the classical Hamiltonian equations and so is subject to a principle of scientific determinism whereby it is known that an initial state a will , after t seconds have elapsed , have passed into a uniquely ...
... assumed to be governed by the classical Hamiltonian equations and so is subject to a principle of scientific determinism whereby it is known that an initial state a will , after t seconds have elapsed , have passed into a uniquely ...
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