Linear Operators: Spectral operators |
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Page 1937
... matrix and a nilpotent operator N = k i = 1 -1 ( 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 ...
... matrix and a nilpotent operator N = k i = 1 -1 ( 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 ...
Page 2011
... matrices  ( s ) = ( âμ ( 8 ) ) whose elements are measurable complex valued functions defined almost everywhere on S but not necessarily bounded . For every set o in Σ and every such matrix  ( s ) we define the matrix ( 1 )  ̧ ( 8 ) ...
... matrices  ( s ) = ( âμ ( 8 ) ) whose elements are measurable complex valued functions defined almost everywhere on S but not necessarily bounded . For every set o in Σ 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 ) -1Mik ( μ ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then Mi ( μ ) depends analytically on μ , 1 ≤ i , k≤n ...
... matrix whose elements are given by the equation ( 5 ) , so that the elements Mμ ) -1Mik ( μ ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then Mi ( μ ) depends analytically on μ , 1 ≤ i , k≤n ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero