Linear Operators: General theory |
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Page 136
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Nelson Dunford, Jacob T. Schwartz. 6 LEMMA . There is a uniquely determined smallest field and a uniquely determined smallest o - field containing a given family of sets . PROOF . There is at least one field , namely the field of all ...
Page 455
... determined by GF . F n = 1 We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in ...
... determined by GF . F n = 1 We can even assert that each continuous linear functional ƒ can be included in a denumerable self - determined set G of functionals . For , if ƒ is determined by the denumerable set G1 , let each functional in ...
Page 657
... determined new state y . Since y is uniquely determined by a and t , a function & on S to S is defined by the equa- tion y = ( x ) . The flow 4 is assumed to have the property that ( i ) t Pt ( $ s ( x ) ) = $ t + s ( x ) , for all ...
... determined new state y . Since y is uniquely determined by a and t , a function & on S to S is defined by the equa- tion y = ( x ) . The flow 4 is assumed to have the property that ( i ) t Pt ( $ s ( x ) ) = $ t + s ( x ) , for all ...
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