## Linear Operators: Spectral operators |

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Page 2121

Similarly , one can introduce A -

scalar operators for an admissible algebra of functions defined on the unit circle

C , or on the real line R , respectively . If S e B ( X ) satisfies 18 " = 0 ( n | " ) as In |

→ 00 ...

Similarly , one can introduce A -

**unitary**and A - self adjoint operators as A -scalar operators for an admissible algebra of functions defined on the unit circle

C , or on the real line R , respectively . If S e B ( X ) satisfies 18 " = 0 ( n | " ) as In |

→ 00 ...

Page 2173

An operator U e B ( X ) which is isometric and maps X onto X is sometimes said to

be a

UM | = 1 for n = 0 , + 1 , + 2 , . . . , ( ii ) o ( U ) $ { de | 111 = 1 } , and ( iii ) | R ( A ...

An operator U e B ( X ) which is isometric and maps X onto X is sometimes said to

be a

**unitary**operator on X . It is easy to see that if U € B ( X ) is**unitary**, then ( i ) |UM | = 1 for n = 0 , + 1 , + 2 , . . . , ( ii ) o ( U ) $ { de | 111 = 1 } , and ( iii ) | R ( A ...

Page 2554

Characterization of completely non -

Acad . Polon . Sci . 11 , 111 - 113 ( 1963 ) . 2 . Note on the

contraction operator . Bull . Acad . Polon . Sci . 11 , 463 – 467 ( 1963 ) . 3 .

Characterization of completely non -

**unitary**contractions in Hilbert spaces . Bull .Acad . Polon . Sci . 11 , 111 - 113 ( 1963 ) . 2 . Note on the

**unitary**dilation of acontraction operator . Bull . Acad . Polon . Sci . 11 , 463 – 467 ( 1963 ) . 3 .

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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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### Common terms and phrases

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