## Linear Operators: Spectral operators |

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Page 2068

It is clear that the linear space Lo = Lin Lo

C of all integrable functions which coincide almost everywhere with a continuous

function clearly

It is clear that the linear space Lo = Lin Lo

**satisfies**( 11 ) . Also the space Lo = LinC of all integrable functions which coincide almost everywhere with a continuous

function clearly

**satisfies**( 11 ) . Example 11 . 12 shows that the space Lo = Lin ...Page 2112

The proof of this theorem is based on an analysis of certain B - spaces of vector

valued analytic functions . We say that T

set U and every sequence { fr } of analytic functions from U to X and X e X such ...

The proof of this theorem is based on an analysis of certain B - spaces of vector

valued analytic functions . We say that T

**satisfies**condition ( B ) if for every openset U and every sequence { fr } of analytic functions from U to X and X e X such ...

Page 2314

This

boundary conditions at t = 1 if tan 8 ( 1 + x ) = k18 . Thus , using the addition

formula for the tangent function , T - dI can only fail to have an inverse if i = 82 ,

where s is ...

This

**satisfies**the boundary condition at t = 0 if tan sa = ko8 , and**satisfies**theboundary conditions at t = 1 if tan 8 ( 1 + x ) = k18 . Thus , using the addition

formula for the tangent function , T - dI can only fail to have an inverse if i = 82 ,

where s is ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane 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 uniformly unique valued vector weakly zero