## Linear Operators: Spectral operators |

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Page 2179

It will first be shown that such algebras A may be decomposed into vector direct

sums of the form A = S R , where R is the radical in A and S is an

scalar type operators which is equivalent to an

It will first be shown that such algebras A may be decomposed into vector direct

sums of the form A = S R , where R is the radical in A and S is an

**algebra**ofscalar type operators which is equivalent to an

**algebra**of continuous functions .Page 2194

Let A , be the

essentially bounded on o ( s ) . It follows from Theorem 10 that A , is a full

of scalar type spectral operators which is equivalent to EB ( 1 , 2 ) . It follows from

the ...

Let A , be the

**algebra**of all operators of the form s f ( a ) E ( d ) where f is E -essentially bounded on o ( s ) . It follows from Theorem 10 that A , is a full

**algebra**of scalar type spectral operators which is equivalent to EB ( 1 , 2 ) . It follows from

the ...

Page 2214

5 , the weakly closed operator

strongly closed

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

5 , the weakly closed operator

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

**algebra**generated by B . Thus every A in W ( B ) is the strong limitof finite 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 | |

31 other sections not shown

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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