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

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Results 1-3 of 91

Page 1990

for some E - measurable and essentially bounded complex

RN Before illustrating the results of the preceding section , we shall examine the

structure of these operators in A and in particular show that many of the ...

for some E - measurable and essentially bounded complex

**valued**function â onRN Before illustrating the results of the preceding section , we shall examine the

structure of these operators in A and in particular show that many of the ...

Page 2092

The single

not have the single

S . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man ( 1 ) gave necessary conditions for

...

The single

**valued**extension property . The example of an operator which doesnot have the single

**valued**extension property that is given in Section 2 is due toS . Kakutani ( see Dunford [ 18 ] ) . Kesel ' man ( 1 ) gave necessary conditions for

...

Page 2409

That is , instead of considering the space L , ( D ) as above , we may consider the

space L , ( D , X ) of all X -

in D and satisfying lo ( 33 ) S 18 ( 2 , 4 ) o dx dy ) * = { S , 18 ( z ) dx dy } ip = 15 ...

That is , instead of considering the space L , ( D ) as above , we may consider the

space L , ( D , X ) of all X -

**valued**Borel - Lebesgue measurable functions definedin D and satisfying lo ( 33 ) S 18 ( 2 , 4 ) o dx dy ) * = { S , 18 ( z ) dx dy } ip = 15 ...

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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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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