Linear Operators: Spectral operators |
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Page 2084
... B ) is analytic for λ # 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( \ ; B ) + R ( \ ; C ) I λ • 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
... B ) is analytic for λ # 0 , prove that C is a quasi - nilpotent operator and that R ( λ ; A ) = R ( \ ; B ) + R ( \ ; C ) I λ • 55 ( McCarthy ) Let T be a spectral operator in a complex B - space X which satisfies the growth condition ...
Page 2193
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
... B - space , for it has been shown by Kakutani [ 15 ] that the sum of two commuting scalar type spectral operators in a space of continuous functions need not be a spectral operator . However , if n = 1 in Corollary 15 , then the Hilbert ...
Page 2484
... B ( c ) Show that + ∞ lim 8 ∞ - + 0 + 3 B ( 8 , σ ) στ ίε do - ∞ + B ( 8 , σ ) do FiπA ( s , 8 ) . σ Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued ...
... B ( c ) Show that + ∞ lim 8 ∞ - + 0 + 3 B ( 8 , σ ) στ ίε do - ∞ + B ( 8 , σ ) do FiπA ( s , 8 ) . σ Let be a Hilbert space , and let B ( S ) be the B - space of all bounded operators in H. Let C ( s , t ) be a B ( S ) -valued ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero