## Linear Operators: Spectral operators |

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Page 2130

For an exposition of ordered topological vector spaces , we refer the reader to the

books of Day [ 12 ] , Kelley and Namioka [ 1 ] , Schaefer [ 18 ] and Peressini [ 1 ] .

The notions of order are ... If X is a real

For an exposition of ordered topological vector spaces , we refer the reader to the

books of Day [ 12 ] , Kelley and Namioka [ 1 ] , Schaefer [ 18 ] and Peressini [ 1 ] .

The notions of order are ... If X is a real

**B**-**space**which is ordered by < , let X ...Page 2193

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

arbitrary

commuting scalar type spectral operators in a space of continuous functions ...

Q . E . D . The preceding corollary is not true if the Hilbert space is replaced by an

arbitrary

**B**-**space**, for it has been shown by Kakutani [ 15 ] that the sum of twocommuting scalar type spectral operators in a space of continuous functions ...

Page 2484

0o , where the norm is as specified in Definition 2 . 13 . ( c ) Show that pto B ( s , o

) pto B ( 8 , 0 ) , do FiTA ( s , s ) . 6 + 0 + 1 - 00 8 - 0 Eie J - 008 - 0 Let H be a

Hilbert space , and let B ( H ) be the

C ...

0o , where the norm is as specified in Definition 2 . 13 . ( c ) Show that pto B ( s , o

) pto B ( 8 , 0 ) , do FiTA ( s , s ) . 6 + 0 + 1 - 00 8 - 0 Eie J - 008 - 0 Let H be a

Hilbert space , and let B ( H ) be the

**B**-**space**of all bounded operators in H . LetC ...

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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