## Linear Operators: Spectral operators |

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Page 1991

In particular , if f is

measurable and thus integrable . For , in this case , the range of f may be covered

with a finite number of open sets G1 , . . . , Gn , each having diameter less than a

given ...

In particular , if f is

**continuous**and has its values in a compact set , it is l -measurable and thus integrable . For , in this case , the range of f may be covered

with a finite number of open sets G1 , . . . , Gn , each having diameter less than a

given ...

Page 2066

ft = fs + + * f we have h ( fz ) h ( f ) = h ( fg + e ) h ( f ) , which shows that c ( 8 + t ) =

c ( s ) c ( t ) , that is , c is a homomorphism of the additive group RN into the

multiplicative group of complex numbers and thus c is a

RN .

ft = fs + + * f we have h ( fz ) h ( f ) = h ( fg + e ) h ( f ) , which shows that c ( 8 + t ) =

c ( s ) c ( t ) , that is , c is a homomorphism of the additive group RN into the

multiplicative group of complex numbers and thus c is a

**continuous**character ofRN .

Page 2448

Suppose that : ( a ) a

M , is given ; ( b ) a

given ; ( c ) a

...

Suppose that : ( a ) a

**continuous**linear mapping q : A → B ( X ) , of norm at mostM , is given ; ( b ) a

**continuous**linear mapping n : A → A , of norm at most M1 , isgiven ; ( c ) a

**continuous**linear mapping 1 : A → B ( x ) , of norm at most M1 , such...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined 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 perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero