## 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 2068

It is clear that the linear space L. = Lin L.

It is clear that the linear space L. = Lin L.

**satisfies**( 11 ) . Also the space Lo = Lin C of all integrable functions which coincide almost everywhere with a continuous function clearly**satisfies**( 11 ) . Example 11.12 shows that the ...Page 2112

An example is given to show that not every operator admits a duality theory of type 1 ; however , if T

An example is given to show that not every operator admits a duality theory of type 1 ; however , if T

**satisfies**the condition : ( a ) N ( F1 , T ) = M ( F2 , T ' ) , if Fis the interior of F2 , then T does admit such a duality theory .Page 2314

This

This

**satisfies**the boundary condition at t = 0 if tan sa = = kos , and**satisfies**the boundary conditions at t = 1 if tan s ( 1 + a ) = k18 . Thus , using the addition formula for the tangent function , T - XI can only fail to have an ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 other sections not shown

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### Common terms and phrases

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 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