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

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Page 2299

Hence we find that for n

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

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

Hence we find that for n

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

; T ) and a bounded operator , it follows that T + 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 ( u ; T ) A S | for u 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 ( u ; T ) A S | for u in V ,

and i

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

Page 2394

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

u ) of the equation to = u o , defined for 0 St < oo and for all

+ , such that oz and os are continuous in t and Me for 0 St < 0 and u

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

u ) of the equation to = u o , defined for 0 St < oo and for all

**sufficiently**small u e P+ , such that oz and os are continuous in t and Me for 0 St < 0 and u

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

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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