## Linear operators: Spectral operators |

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Results 1-3 of 92

Page 1979

It follows from equations (iv) and (v) of Lemma 3 that E(Xli{s); A(s)) is e-

essentially bounded on S. Lemma 4 then

is satisfied. Q.E.D. 8 Corollary. Every operator A in W is the strong limit of a

sequence of ...

It follows from equations (iv) and (v) of Lemma 3 that E(Xli{s); A(s)) is e-

essentially bounded on S. Lemma 4 then

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

sequence of ...

Page 2169

This

continuous function g. A repetition of this argument

and g are both bounded Borel functions. Thus the operators /(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 /and g are both bounded Borel functions. Thus the operators /(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 ((od — T)z, (od — 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 ((od — T)z, (od — T)x)

**shows**that \(od - T)x\2 = \J(<x)x\2 + |(#(a)/ - 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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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 commuting compact complex numbers complex plane constant contains continuous functions converges Corollary countably additive Definition denote dense differential operator disjoint Doklady Akad domain eigenvalues elements equation exists finite number Foias follows from Lemma follows from Theorem formal differential operator formula Hence Hilbert space hypothesis identity inequality inverse Lebesgue Math matrix measurable functions multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial 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