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

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Page 2299

Hence we find that for n

u ; T + P ) = Blu ) . Since Blu ) is clearly the product of the compact operator R ( u ;

T ) and a bounded operator , it follows that I + P is a discrete operator .

Hence we find that for n

**sufficiently**large , each u in Cn is in plT + P ) and that R (u ; T + P ) = Blu ) . Since Blu ) is clearly the product of the compact operator R ( u ;

T ) and a bounded operator , it follows that I + P is a discrete operator .

Page 2360

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. It will be shown below that | T''R ( y ; T ) A | } for p in V , and i

Spectral Theory : Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob

Theodore Schwartz. It will be shown below that | T''R ( y ; T ) A | } for p in V , and i

**sufficiently**large . From this it will then follow as above that the function f ( u ) R ...Page 2394

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

j ) of the equation to ru'o , defined for 0 St < oo and for all

, such that og and os are continuous in t and u for 0 St < oo and u

Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oz ( t ,

j ) of the equation to ru'o , defined for 0 St < oo and for all

**sufficiently**small ue P +, such that og and os are continuous in t and u for 0 St < oo and u

**sufficiently**...### What people are saying - Write a review

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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 defined Definition denote dense determined differential operator discrete 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