## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Results 1-3 of 88

Page 2203

Let e be an open

and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed

with ...

Let e be an open

**subset**of 1 , let x and 2 * be elements of X , X * , respectively ,and let z > 0 . Then , because of the regularity of xA ( • ) x * , there is a closed

**subset**8 of e such that ( i ) | A ( 81 ) * * — XA ( e ) * * / < E , for every Borel set & ,with ...

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 ) = { z12 - 1€ 0 } is a compact

...

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 ) = { z12 - 1€ 0 } is a compact

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

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

defined 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 functiondefined in RX ...

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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### Common terms and phrases

analytic apply arbitrary assumed B-space Banach space Boolean algebra Borel sets boundary conditions bounded bounded Borel bounded operator Chapter clear clearly closure commuting compact complex consider constant contained converges Corollary corresponding countably additive defined Definition denote dense determined differential operator 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 positive preceding present problem projections PROOF properties prove range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows spectral measure spectral operator spectrum statement strongly subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero