Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 2133
... remarks , and applications . We remark only that the notion of the index arose in 1921 in connection with the study of certain singular integral equations by F. Noether . In essence , the first stability theorem was proved by Dieudonné ...
... remarks , and applications . We remark only that the notion of the index arose in 1921 in connection with the study of certain singular integral equations by F. Noether . In essence , the first stability theorem was proved by Dieudonné ...
Page 2295
... remark following Lemma 2 that E ( \ - 1 ; T - 1 ) = 0 . It then follows from the first assertion of Theorem VII.3.20 that A - 1 is in p ( T - 1 ) . Consequently , according to the remark following Lemma 2 , λ o ( T ) , which is contrary ...
... remark following Lemma 2 that E ( \ - 1 ; T - 1 ) = 0 . It then follows from the first assertion of Theorem VII.3.20 that A - 1 is in p ( T - 1 ) . Consequently , according to the remark following Lemma 2 , λ o ( T ) , which is contrary ...
Page 2296
... remark following Lemma 2 that -1 ( μIT ) -1f = μ - 1π - 1μ - 1I — T - 1 ) -1ƒ , μ έ σ ( Τ ) . Since , by this same remark , E ( \ ¡ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1IT - 1 ) -1f is analytic whenever μ 0 ...
... remark following Lemma 2 that -1 ( μIT ) -1f = μ - 1π - 1μ - 1I — T - 1 ) -1ƒ , μ έ σ ( Τ ) . Since , by this same remark , E ( \ ¡ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1IT - 1 ) -1f is analytic whenever μ 0 ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero