Linear Operators, Part 2 |
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Page 1937
... matrix and a nilpotent operator N == ( Tλ , 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 nilpotent ...
... matrix and a nilpotent operator N == ( Tλ , 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 nilpotent ...
Page 2011
... matrices  ( s ) = ( ( s ) ) whose elements are measurable complex valued functions defined almost everywhere on S but not necessarily bounded . For every set σ in Σ 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 σ 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 ) -1M ( μ ) are those of the inverse matrix of the matrix defined by the equation ( 5 ) . Then Mik ( ) depends analytically on μ , 1i , k≤n . 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 Mik ( ) depends analytically on μ , 1i , k≤n . Consider the ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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 Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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