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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Results 1-3 of 43
Page 1926
... normal operator , then ( T — λI ) E ( X ) = 0 and this formula reduces to the formula f ( T ) = f ( x ) E ( X ) , λεσ ( Τ ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these two ...
... normal operator , then ( T — λI ) E ( X ) = 0 and this formula reduces to the formula f ( T ) = f ( x ) E ( X ) , λεσ ( Τ ) which is not valid for an arbitrary T. To see more clearly the difference between the calculi given by these two ...
Page 1978
... operators , we observe that a self adjoint operator or , more generally , a normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p xp matrix  ( s ) ...
... operators , we observe that a self adjoint operator or , more generally , a normal operator in A is a spectral operator . For if A is a normal operator in A " , it follows from Theorem 9.3 that for e - almost all s in the p xp matrix  ( s ) ...
Page 2005
... operator A in A2 , not of the form A = λ with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
... operator A in A2 , not of the form A = λ with λ in A , has a non - zero radical part if e ( S1 ) 0. By Theo- rem 6.4 the spectral operators with non - zero radical parts are the only ones not similar to normal operators . Thus both of ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero