## Linear Operators: Spectral operators |

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Page 2313

This is because in Hilbert space we use the Hermitian rather than the pure

the effect of introducing complex conjugates in many of the Hilbert - space

formulas ...

This is because in Hilbert space we use the Hermitian rather than the pure

**Banach space**adjoint , contrary to our practice in other**Banach spaces**. This hasthe effect of introducing complex conjugates in many of the Hilbert - space

formulas ...

Page 2539

Spectral operators on locally convex spaces . Bull . Amer . Math . Soc . 67 , 125 –

128 ( 1961 ) . 4 . Scalar dilations and scalar extensions of operators on

...

Spectral operators on locally convex spaces . Bull . Amer . Math . Soc . 67 , 125 –

128 ( 1961 ) . 4 . Scalar dilations and scalar extensions of operators on

**Banach****spaces**( I ) . J . Math . Mech . 14 , 841 - 856 ( 1965 ) . 5 . Notes on spectral theory...

Page 2541

Trans . Amer . Math . Soc . 111 , 152 – 181 ( 1964 ) . 5 . Classification of operators

by means of their operational calculus . Trans . Amer . Soc . 115 , 194 - 224 (

1965 ) . 6 . A Jordan decomposition for operators in

Trans . Amer . Math . Soc . 111 , 152 – 181 ( 1964 ) . 5 . Classification of operators

by means of their operational calculus . Trans . Amer . Soc . 115 , 194 - 224 (

1965 ) . 6 . A Jordan decomposition for operators in

**Banach space**. Bull . Amer .### What people are saying - Write a review

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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