## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Results 1-3 of 29

Page 1972

( G ) = 1 - 1 ( 17 ( G ) ) , which shows that , is -

E -

# 8x + 1 ( 8 ) = . = 8 , ( 8 ) # fg + 1 ( 8 ) = . . = { p ( s ) } , k = 1 isksj < p and so on ...

( G ) = 1 - 1 ( 17 ( G ) ) , which shows that , is -

**measurable**. ... Let 8 → [ ( 8 ) be aE -

**measurable**map from S into B ( EP ) . ... ( 8 ) } , Si =**U**{ s ! $ , ( s ) = . . . = f ( s )# 8x + 1 ( 8 ) = . = 8 , ( 8 ) # fg + 1 ( 8 ) = . . = { p ( s ) } , k = 1 isksj < p and so on ...

Page 2188

( 1 ) Now the set of bounded Borel

du ) = 9 ( F ( A ) ) E ( DA ) J $ ( 1 ) is clearly linear and closed in the set of all

bounded Borel functions . Since this set contains every characteristic function of a

...

( 1 ) Now the set of bounded Borel

**measurable**functions g for which s g (**u**) Ez (du ) = 9 ( F ( A ) ) E ( DA ) J $ ( 1 ) is clearly linear and closed in the set of all

bounded Borel functions . Since this set contains every characteristic function of a

...

Page 2405

Next , let h be a non - negative

Hölder ' s inequality we have ( 13 ) SS14 ( s , t ) / n ( € ) u ( dt ) ? relds ) < S : { { {

448 , € ) 1 " pe ( de ) " s prelep ( at ) u ( da ) = { AXS1n0 ) * ( dr ) . If he L ; ( S , E , p

) ...

Next , let h be a non - negative

**u**-**measurable**function defined on S . Then , byHölder ' s inequality we have ( 13 ) SS14 ( s , t ) / n ( € ) u ( dt ) ? relds ) < S : { { {

448 , € ) 1 " pe ( de ) " s prelep ( at ) u ( da ) = { AXS1n0 ) * ( dr ) . If he L ; ( S , E , p

) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

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