Linear Operators: Spectral operators |
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Page 2299
... sufficiently large and for μ in C1 , we have - | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 1 -m ≤ 2M dñ1 Ĉ ( [ \ n ] + d „ ) TM o dà TM ( 2M | A | ) m m = 1 ≤ 8M2 | A | dñ 2 ...
... sufficiently large and for μ in C1 , we have - | R ( μ ; T + P ) — R ( μ ; T ) | = | B ( μ ) — R ( μ ; T ) | since for sufficiently large n , 00 1 -m ≤ 2M dñ1 Ĉ ( [ \ n ] + d „ ) TM o dà TM ( 2M | A | ) m m = 1 ≤ 8M2 | A | dñ 2 ...
Page 2300
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is not one of the points μ ,, n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
... sufficiently large p . Since E is a count- ably additive spectral resolution , we have E ( μ ; T + P ) ( I − E , ) = 0 if μ is not one of the points μ ,, n ≥ K. It follows from Lemma 3 that o ( T + P ) consists of the union of the ...
Page 2394
... sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e - itu ; σ ' ' ( t , μ ) ~ —iμe - itu ; as t → ∞ , for all μ Є P✦ such that I ( μ ) ...
... sufficiently small μ € P + , such that σ , and og are continuous in t and μ for 0 ≤t < ∞ and μ sufficiently small , and such that σз ( t , μ ) ~ e - itu ; σ ' ' ( t , μ ) ~ —iμe - itu ; as t → ∞ , for all μ Є P✦ such that I ( μ ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero