## Linear Operators: Spectral operators |

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Results 1-3 of 84

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

Since t + f1 is a

Since fs * fr = fs + + * f we have h ( fr ) h ( ft ) = h ( fs + t ) h ( f ) , which shows that c

( 8 + t ) ...

Since t + f1 is a

**continuous**map of RN into Li ( XI . 3 . 1 ( f ) ) and since h is**continuous**( IX . 2 . 3 ) , the inequality ( 7 ) shows that c ( t ) is**continuous**in t .Since fs * fr = fs + + * f we have h ( fr ) h ( ft ) = h ( fs + t ) h ( f ) , which shows that c

( 8 + t ) ...

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 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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### Common terms and phrases

adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero