## 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 B be a

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 a

Boolean ...

Page 2194

Let 2Ij be the

bounded on a(S). It follows from Theorem 10 that 9Ii is a full

type spectral operators which is equivalent to EB(A, E). It follows from the

definition ...

Let 2Ij be the

**algebra**of all operators of the form $ f(\)E(d\) where / is ^-essentiallybounded on a(S). It follows from Theorem 10 that 9Ii is a full

**algebra**of scalartype spectral operators which is equivalent to EB(A, E). It follows from the

definition ...

Page 2214

1.5, the weakly closed operator

strongly closed

finite linear combinations of elements of B. It follows that A leaves invariant ...

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 ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator Akad Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets bounded bounded operator Chapter clear closed commuting compact complex consider constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity Nauk norm normal 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 subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero