## Linear Operators: Spectral operators |

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Results 1-3 of 90

Page 1979

It follows from equations (iv) and (v) of Lemma 3 that ^(Ai;(s); A(s)) is e-essentially

bounded on S. Lemma 4 then

Q.E.D. 8 Corollary. Every operator A in 21 p is the strong limit of a sequence of ...

It follows from equations (iv) and (v) of Lemma 3 that ^(Ai;(s); A(s)) is e-essentially

bounded on S. Lemma 4 then

**shows**that condition (i) of the theorem is satisfied.Q.E.D. 8 Corollary. Every operator A in 21 p is the strong limit of a sequence of ...

Page 2169

This

continuous function g. A repetition of this argument

g are both bounded Borel functions. Thus the operators f(T) and g(T) commute

and also, ...

This

**shows**that (vi) holds for every bounded Borel function / and everycontinuous function g. A repetition of this argument

**shows**that it also holds if/ andg are both bounded Borel functions. Thus the operators f(T) and g(T) commute

and also, ...

Page 2170

These lemmas will

self adjoint operator in Hilbert space. ... If a is not real, an expansion of the scalar

product ((a/ — T)x, (ocl — T)x)

These lemmas will

**show**that the hypotheses of Theorem 5.18 are satisfied by aself adjoint operator in Hilbert space. ... If a is not real, an expansion of the scalar

product ((a/ — T)x, (ocl — T)x)

**shows**that | (a/ - T)x\2 = | J(ct)x\* + \(£(<x)I - T)x\2 ...### What people are saying - Write a review

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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