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

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Results 1-3 of 67

Page 1979

The

A EX HP , and Axl ( i - - Ex ) HP = 0 , both spectral operators . Hence Theorem 3 .

10 shows that Al is a spectral operator . Now since SK → S it follows ...

The

**corresponding**operator Ax = SS Â ( s ) e ( ds ) has its restrictions Ax EK HP =A EX HP , and Axl ( i - - Ex ) HP = 0 , both spectral operators . Hence Theorem 3 .

10 shows that Al is a spectral operator . Now since SK → S it follows ...

Page 2292

The set of all vectors f satisfying the equation ( T - 107 ) " 0f = 0 is a finite

dimensional linear space , called the space of generalized eigenvectors of T

function of T ...

The set of all vectors f satisfying the equation ( T - 107 ) " 0f = 0 is a finite

dimensional linear space , called the space of generalized eigenvectors of T

**corresponding**to the eigenvalue do . If Eldo ; T ) = E ( 20 ) is the idempotentfunction of T ...

Page 2305

8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each

eigenspace

immediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

8 , 0 ( L ) is the set of numbers in = ( n tæt B + 1 ) ( n + & + B ) , and each

eigenspace

**corresponding**to these eigenvalues is one - dimensional . It followsimmediately from Corollary 9 that L + B is a spectral operator for each bounded

operator ...

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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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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 formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal 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