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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional 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 Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ