## Linear Operators: Spectral operators |

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Page 1937

E(A() which is equivalent to a diagonal

— Xi I)E(Xt). Stated in other terms, this classical reduction of Jordan asserts that

every finite square

E(A() which is equivalent to a diagonal

**matrix**and a nilpotent operator N = Vf. x (T— Xi I)E(Xt). 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 ...Page 2011

The notation will be that of the preceding section, but we shall now be concerned

with pxp

... For every set a in E and every such

The notation will be that of the preceding section, but we shall now be concerned

with pxp

**matrices**A(s) = (dik(s)) whose elements are measurable complex valued... For every set a in E and every such

**matrix**A (s) we define the**matrix**(1) i.Page 2327

... cofactor of the element Mik(yi) in the

equation (5), so that the elements M (/jl) ~ 1Mtk{fi) are those of the inverse

of the

...

... cofactor of the element Mik(yi) in the

**matrix**whose elements are given by theequation (5), so that the elements M (/jl) ~ 1Mtk{fi) are those of the inverse

**matrix**of the

**matrix**defined by the equation (5). Then JStk(fj.) depends analytically on (j.,...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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### Common terms and phrases

adjoint operator algebra of projections Amer analytic arbitrary asymptotic B-space Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator bounded spectral commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote differential operator disjoint Doklady Akad domain eigenvalues elements equation equivalent exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial preceding Proof properties prove quasi-nilpotent restriction Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset Suppose trace class type spectral operator unbounded uniformly bounded unique vector weakly complete zero