## Linear Operators: Spectral operators |

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Page 2179

The uniformly closed

continuous f unctions on its own space of maximal ideals. Proof. Let

Boolean ...

The uniformly closed

**algebra**of operators generated by a bounded Boolean**algebra**of projection operators is a full**algebra**equivalent to the**algebra**ofcontinuous f unctions on its own space of maximal ideals. Proof. Let

**B**be aBoolean ...

Page 2193

It follows from Corollary XV.6.3 that the projections generating 93 are all

contained in a bounded Boolean

decomposition of 91 follows from Theorem 3. The final assertion follows from

Corollary 14.

It follows from Corollary XV.6.3 that the projections generating 93 are all

contained in a bounded Boolean

**algebra B**of projections, and thus the desireddecomposition of 91 follows from Theorem 3. The final assertion follows from

Corollary 14.

Page 2214

1.5, the weakly closed operator

strongly closed

finite linear combinations of elements of

1.5, the weakly closed operator

**algebra**2B(**B**) generated by**B**is the same as thestrongly closed

**algebra**generated by**B**. Thus every A in W(**B**) is the strong limit offinite linear combinations of elements of

**B**. It follows that A leaves invariant ...### What people are saying - Write a review

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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