Linear Operators: General theory |
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Page 572
... set of spheres S ( α1 , ε ( α1 ) ) , . . . , S ( an , ε ( an ) ) will cover σ ( T ) . If some sphere S ( α ,, ε ( α ; ) ) contains an infinite number of points of o ... spectral sets form a Boolean 572 VII.3.17 VII . GENERAL SPECTRAL THEORY.
... set of spheres S ( α1 , ε ( α1 ) ) , . . . , S ( an , ε ( an ) ) will cover σ ( T ) . If some sphere S ( α ,, ε ( α ; ) ) contains an infinite number of points of o ... spectral sets form a Boolean 572 VII.3.17 VII . GENERAL SPECTRAL THEORY.
Page 573
Nelson Dunford, Jacob T. Schwartz. It is evident that the spectral sets form a Boolean algebra of subsets of o ( T ) . If σ is a spectral set , there is a function ƒ e F ( T ) which is identically one on σ and which vanishes on the rest ...
Nelson Dunford, Jacob T. Schwartz. It is evident that the spectral sets form a Boolean algebra of subsets of o ( T ) . If σ is a spectral set , there is a function ƒ e F ( T ) which is identically one on σ and which vanishes on the rest ...
Page 574
... spectral set of f ( T ) . Then o ( T ) f1 ( t ) is a spectral set of T , and - E ( t ; f ( T ) ) = E ( ƒ ̃1 ( t ) ; T ) . PROOF . Let e ( u ) = 1 for u in a neighborhood of t , and let e , ( u ) = 0 for u in a neighborhood of the rest ...
... spectral set of f ( T ) . Then o ( T ) f1 ( t ) is a spectral set of T , and - E ( t ; f ( T ) ) = E ( ƒ ̃1 ( t ) ; T ) . PROOF . Let e ( u ) = 1 for u in a neighborhood of t , and let e , ( u ) = 0 for u in a neighborhood of the rest ...
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