## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 1926

If T is a normal operator , then ( T - AI ) E ( A ) = 0 and this formula reduces to the formula f ( T ) = E f ( a ) E ( a ) , λεσ ( Τ ) which is not valid for an

If T is a normal operator , then ( T - AI ) E ( A ) = 0 and this formula reduces to the formula f ( T ) = E f ( a ) E ( a ) , λεσ ( Τ ) which is not valid for an

**arbitrary**T. To see more clearly the difference between the calculi given ...Page 2101

This was proved by Dunford [ 18 ] ; however , McCarthy [ 1 , I ] showed that this assertion does not hold in an

This was proved by Dunford [ 18 ] ; however , McCarthy [ 1 , I ] showed that this assertion does not hold in an

**arbitrary**B - space . In fact , all that can be inferred in an**arbitrary**...Page 2193

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

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 two commuting scalar type spectral operators in a space of continuous ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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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 defined Definition denote dense determined differential operator discrete 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