## Linear Operators: Spectral operators |

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Page 2256

Since o ( T ) is totally disconnected , each point in o ( T ) is contained in an

arbitrarily small compact

of o ( T ) . It follows that the set t ( o ) = { 212 - 1€ o } is a compact

open ...

Since o ( T ) is totally disconnected , each point in o ( T ) is contained in an

arbitrarily small compact

**subset**o of o ( T ) which is open in the relative topologyof o ( T ) . It follows that the set t ( o ) = { 212 - 1€ o } is a compact

**subset**of o ( R ) ,open ...

Page 2257

3 that Elo ; T ' ) = E ( + ( 0 ) ; R ) for each compact spectral set o of T . Moreover , it

is clear that as o runs over the family K of all compact open

) runs over the family of all compact open

3 that Elo ; T ' ) = E ( + ( 0 ) ; R ) for each compact spectral set o of T . Moreover , it

is clear that as o runs over the family K of all compact open

**subsets**of olT ' ) , 7 ( o) runs over the family of all compact open

**subsets**of o ( R ) which do not ...Page 2309

Our next step is consequently to define such series and develop some of their

basic properties . 4 DEFINITION . ( a ) Let R be an unbounded

complex plane . Let R be a

in RX ...

Our next step is consequently to define such series and develop some of their

basic properties . 4 DEFINITION . ( a ) Let R be an unbounded

**subset**of thecomplex plane . Let R be a

**subset**of the complex plane , and f a function definedin RX ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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adjoint operator analytic apply arbitrary assume B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded operator Chapter clear closed commuting compact complex consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator discrete domain elements equation equivalent established example exists extension fact finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm 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 uniform uniformly unique valued vector weakly zero