Linear Operators: General theory |
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Page 51
... neighborhood of f ( x ) . If U is a neighborhood of a such that f ( U ) CVf ( y - 1x ) , then Ux - 1y is a neighborhood of y such that f ( Ux - 1y ) = f ( U ) f ( x − 1y ) C Vƒ ( y ̄1x ) f ( x - 1y ) = V. Therefore , f is con- tinuous ...
... neighborhood of f ( x ) . If U is a neighborhood of a such that f ( U ) CVf ( y - 1x ) , then Ux - 1y is a neighborhood of y such that f ( Ux - 1y ) = f ( U ) f ( x − 1y ) C Vƒ ( y ̄1x ) f ( x - 1y ) = V. Therefore , f is con- tinuous ...
Page 56
... neighborhood M of 0 such that M - MCG . For every xe X , x / n → 0 , and so a enM for large n . Thus ∞ X = UnM , Y ... neighborhood of 0. Thus the closure of the image of a neighborhood of the origin contains a neighborhood of the ...
... neighborhood M of 0 such that M - MCG . For every xe X , x / n → 0 , and so a enM for large n . Thus ∞ X = UnM , Y ... neighborhood of 0. Thus the closure of the image of a neighborhood of the origin contains a neighborhood of the ...
Page 572
... neighborhood of 2. Then , since f ( σ ( T ) ) = 0 , ƒ has a zero of finite order n at . Conse- 2 . quently , the function g1 , defined by g1 ( § ) = ( 21 — § ) " / ƒ ( § ) , is analytic in a neighborhood of 2. Let e be a function ...
... neighborhood of 2. Then , since f ( σ ( T ) ) = 0 , ƒ has a zero of finite order n at . Conse- 2 . quently , the function g1 , defined by g1 ( § ) = ( 21 — § ) " / ƒ ( § ) , is analytic in a neighborhood of 2. Let e be a function ...
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