Linear Operators: Spectral operators |
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Page 2203
... basis for the topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 4 , and since B generates ( B ) , the sets σ ( E ) form a ...
... basis for the topology in 4. To see this , note that sets of the form { || ( T - 1A ) ( λ ) | < a } , with A in A ( B ) form , by definition , a subbasis for the topology of 4 , and since B generates ( B ) , the sets σ ( E ) form a ...
Page 2451
... basis , we have 00 ( 14 ) ΣΣ n = 1 m = 1 \ m #n ( Xm A * xn ) An - Am ( x , xm ) VII ∞ n = 1 2 00 m = 1 m # n 2 Σ ( 2 , 2m ) 2 m = 1 \ n m 00 2 ≤ | x | 2 Σ rñ2 | ( Axm , Xn ) | 2 . n , m = 1 Therefore , by Lemma IV.4.9 and Corollary ...
... basis , we have 00 ( 14 ) ΣΣ n = 1 m = 1 \ m #n ( Xm A * xn ) An - Am ( x , xm ) VII ∞ n = 1 2 00 m = 1 m # n 2 Σ ( 2 , 2m ) 2 m = 1 \ n m 00 2 ≤ | x | 2 Σ rñ2 | ( Axm , Xn ) | 2 . n , m = 1 Therefore , by Lemma IV.4.9 and Corollary ...
Page 2503
... basis of rather general hypo- theses . Related results are given in Birman [ 3 ] . In this paper , theorems of the nature of the wave operator invariance theorem are used to establish the existence of the limits lim , etH2e - ti on the ...
... basis of rather general hypo- theses . Related results are given in Birman [ 3 ] . In this paper , theorems of the nature of the wave operator invariance theorem are used to establish the existence of the limits lim , etH2e - ti on the ...
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