## 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{ktj(s); A(s)) is e-essentially

bounded on S. Lemma 4 then

Q.E.D. 8 Corollary. Every operator A in 91" is the strong limit of a sequence of ...

It follows from equations (iv) and (v) of Lemma 3 that E{ktj(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 91" 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 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 /and g are both bounded Borel functions. Thus the operators f(T) and g(T)

commute and also, ...

Page 2170

lemmas will be needed. These lemmas will

5.18 are satisfied by a self adjoint operator in Hilbert space. ... \S(*)\ Proof. If a is

not real, an expansion of the scalar product ((od — T)x, (od — T)x)

lemmas will be needed. These lemmas will

**show**that the hypotheses of Theorem5.18 are satisfied by a self adjoint operator in Hilbert space. ... \S(*)\ Proof. If a is

not real, an expansion of the scalar product ((od — T)x, (od — T)x)

**shows**that ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectra Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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adjoint operator Akad Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets bounded bounded operator Chapter clear closed commuting compact complex consider constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity Nauk norm perturbation plane positive preceding present problem projections Proof properties prove range resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero