## Linear Operators: Spectral operators |

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Page 1936

... if and only if each

... if and only if each

**restriction**T | E ; X is a spectral operator . ... X is the corresponding**restriction**of the resolution of the identity for T. PROOF ...Page 2094

**Restrictions**and quotients . Theorem 3.10 shows that if a spectral operator Te B ( X ) is reduced by a closed subspace Y SX and one of its complements ...Page 2228

If o is a Borel set , and T is a spectral operator with resolution of the identity E , then the

If o is a Borel set , and T is a spectral operator with resolution of the identity E , then the

**restriction**T | E ( 0 ) X of T to E ( 0 ) X is a spectral ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

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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 countably additive defined Definition denote dense determined differential operator 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