## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Page 2068

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

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

function clearly

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

**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 { fn } 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 { fn } of analytic functions from U to X and X e X such ...

Page 2399

Then the equation to = 0 has two solutions o , and 0 satisfying the asymptotic

relationships Oi ( t ) ~ 1 , oz ( t ) ~ t as t→0 . Proof . We saw in Corollary 2 that o ( t

) = 0 ( t , 0 )

that ...

Then the equation to = 0 has two solutions o , and 0 satisfying the asymptotic

relationships Oi ( t ) ~ 1 , oz ( t ) ~ t as t→0 . Proof . We saw in Corollary 2 that o ( t

) = 0 ( t , 0 )

**satisfies**the first of these asymptotic relationships . Let a be so largethat ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 manifold Math Moreover multiplicity norm positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero