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 1937
... matrix and a nilpotent operator N == ( T — λ , I ) E ( ) , ) . Stated in other terms , this classical reduction of Jordan asserts that every finite square matrix of complex numbers is equivalent to the sum of a diagonal matrix and a ...
... matrix and a nilpotent operator N == ( T — λ , I ) E ( ) , ) . Stated in other terms , this classical reduction of Jordan asserts that every finite square matrix of complex numbers is equivalent to the sum of a diagonal matrix and a ...
Page 2011
... matrices  ( s ) = ( ( s ) ) whose elements are measurable complex valued functions defined almost everywhere on S but not necessarily bounded . For every set o in E and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( 8 ) =  ...
... matrices  ( s ) = ( ( s ) ) whose elements are measurable complex valued functions defined almost everywhere on S but not necessarily bounded . For every set o in E and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( 8 ) =  ...
Page 2327
... matrix whose elements are given by the equation ( 5 ) , so that the elements Mμ ) -1M ( μ ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then Mμ ) depends analytically on μ , 1i , kn . Consider the ...
... matrix whose elements are given by the equation ( 5 ) , so that the elements Mμ ) -1M ( μ ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then Mμ ) depends analytically on μ , 1i , kn . Consider the ...
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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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