Linear Operators: General theory |
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Nelson Dunford, Jacob T. Schwartz. in A has a neighborhood containing at most a finite number of a ,. Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A ...
Nelson Dunford, Jacob T. Schwartz. in A has a neighborhood containing at most a finite number of a ,. Since a finite number of these neighborhoods cover A , the sequence { a } consists of only a finite number of distinct points of A ...
Page 428
... a finite set of elements BC such that | B | ≤1 / n and such that ( An UB2 ) o ( n + 1 ) S * CU . n If this is not the case , it is clear that the family of sets of the form ( An UB ) ° ○ ( n + 1 ) S * ○ U ' where B is finite and | B | ≤ ...
... a finite set of elements BC such that | B | ≤1 / n and such that ( An UB2 ) o ( n + 1 ) S * CU . n If this is not the case , it is clear that the family of sets of the form ( An UB ) ° ○ ( n + 1 ) S * ○ U ' where B is finite and | B | ≤ ...
Page 556
Nelson Dunford, Jacob T. Schwartz. 1. Spectral Theory in a Finite Dimensional Space Throughout this section , X will denote a finite dimensional com- plex B - space , and T a linear operator in B ( X ) . Our aim is to study the algebraic ...
Nelson Dunford, Jacob T. Schwartz. 1. Spectral Theory in a Finite Dimensional Space Throughout this section , X will denote a finite dimensional com- plex B - space , and T a linear operator in B ( X ) . Our aim is to study the algebraic ...
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