Linear Operators: General theory |
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Page 36
... independent set . The cardinality of a Hamel basis is a number independent of the Hamel basis ; it is called the dimension of the linear space . This independence is readily proved if there is a finite Hamel basis , in which case the ...
... independent set . The cardinality of a Hamel basis is a number independent of the Hamel basis ; it is called the dimension of the linear space . This independence is readily proved if there is a finite Hamel basis , in which case the ...
Page 251
... independent of the order in which its terms are arranged . PROOF . For m > n m m m | Σ α , y ; 2 = ( Σ α¡y1 , Σ α ̧y ; ) i = n i = n j = n m m m - Σ Σαά ; ( 1 ) ; ) Σ x 2 , i = n i = n j = n and so the one series converges if the other ...
... independent of the order in which its terms are arranged . PROOF . For m > n m m m | Σ α , y ; 2 = ( Σ α¡y1 , Σ α ̧y ; ) i = n i = n j = n m m m - Σ Σαά ; ( 1 ) ; ) Σ x 2 , i = n i = n j = n and so the one series converges if the other ...
Page 601
... independent of the choice of a in o ( T ) . Let V be an open set containing o ( T ) whose boundary г consists of a finite number of Jordan arcs and such that f is analytic on VUI . Let I have positive orientation with respect to the ...
... independent of the choice of a in o ( T ) . Let V be an open set containing o ( T ) whose boundary г consists of a finite number of Jordan arcs and such that f is analytic on VUI . Let I have positive orientation with respect to the ...
Contents
Preliminary Concepts | 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 ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element ergodic exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ