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

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Page 2066

Since tnft is a

that c ( t ) is

additive group RN onto the multiplicative group of the unit circle in the complex

plane ...

Since tnft is a

**continuous**map of RN into Li ( XI . ... 3 ) , the inequality ( 7 ) showsthat c ( t ) is

**continuous**in t . ... Thus c is a**continuous**homomorphism of theadditive group RN onto the multiplicative group of the unit circle in the complex

plane ...

Page 2443

1 p 24 THEOREM . Let 1 sp < , and let Lp [ 0 , 1 ] be the space of all complex

valued , Borel - Lebesgue measurable functions defined in [ 0 , 1 ] and satisfying {

$ 15 ( 2 ) | P dx } " * = \ s \ < . Let g ( x , y ) be defined and

triangle ...

1 p 24 THEOREM . Let 1 sp < , and let Lp [ 0 , 1 ] be the space of all complex

valued , Borel - Lebesgue measurable functions defined in [ 0 , 1 ] and satisfying {

$ 15 ( 2 ) | P dx } " * = \ s \ < . Let g ( x , y ) be defined and

**continuous**on thetriangle ...

Page 2448

Suppose that : ( a ) a

M , is given ; ( b ) a

given ; ( c ) a

such ...

Suppose that : ( a ) a

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

**continuous**linear mapping n : 4 →A , of norm at most M1 , isgiven ; ( c ) a

**continuous**linear mapping T : A → B ( X ) , of norm at most M 1 ,such ...

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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