## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2169

This shows that ( vi ) holds for every

continuous function g . A repetition of this argument shows that it also holds if f

and g are both

commute and ...

This shows that ( vi ) holds for every

**bounded**Borel function f and everycontinuous function g . A repetition of this argument shows that it also holds if f

and g are both

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

Page 2239

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. Since f Xe is a bounded function , the operator T ( f Xe ) is a

**bounded operator**. If x is in E ( 7 ) X as well as in E ( e ) X , it follows from the ...Page 2252

An attempt to follow the development in the

runs into difficulties . The

quasi - nilpotent restriction to each space E ( o ) X with o

An attempt to follow the development in the

**bounded**case by writing N = T - Sruns into difficulties . The

**operator**N , although easily seen by Lemma 2 to have aquasi - nilpotent restriction to each space E ( o ) X with o

**bounded**, need not be ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero