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 1940
... determined by T. Hence N = T - S is uniquely determined by T. It follows from Lemma 4 that T and S have the same spectrum . Next it will be shown that every spectral operator T has the desired decomposition . The operators S and N are ...
... determined by T. Hence N = T - S is uniquely determined by T. It follows from Lemma 4 that T and S have the same spectrum . Next it will be shown that every spectral operator T has the desired decomposition . The operators S and N are ...
Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фр Ф T1 ( q ) = [ _ _p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фр Ф T1 ( q ) = [ _ _p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
Page 2373
... determine discrete differential operators having eigenvalues λ = s2 determined by equations of the form sin 8 = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + ... , the ratio of a and b being ...
... determine discrete differential operators having eigenvalues λ = s2 determined by equations of the form sin 8 = ks . In this case the eigenvalues are located asymptotically at the points an2 + ibn In n + ... , the ratio of a and b being ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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