## Linear Operators: Spectral operators |

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Page 2312

Let do be a spectral point of the discrete operator T in a B - space X. Let fi , f2 , ... ,

f * be a basis for the solutions of the ... It is well to remark , however , that in the

special case in which the

Let do be a spectral point of the discrete operator T in a B - space X. Let fi , f2 , ... ,

f * be a basis for the solutions of the ... It is well to remark , however , that in the

special case in which the

**Banach space**is Hilbert space , the usual distinction ...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 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 . Math .### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero