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

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Page 1926

... λεσ ( Τ ) which is not valid for an

... λεσ ( Τ ) which is not valid for an

**arbitrary**T. To see more clearly the difference between the calculi given by these two formulas , let us rewrite ...Page 1941

By the above , this shows that o ( N ) C . , and since & > 0 is

By the above , this shows that o ( N ) C . , and since & > 0 is

**arbitrary**, it follows that a ( N ) = { 0 } . It then follows from Corollary 3 that N is a ...Page 1963

Let S be an

Let S be an

**arbitrary**set and Ea o - field of sets in S with Sin E. Let e ( ' ) be a countably XV.9 1963 THE ALGEBRAS AP AND ŪP.### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

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adjoint operator Amer analytic applications arbitrary assume B-space Banach space belongs Boolean algebra Borel sets 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 example exists extension fact finite follows formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math measure Moreover multiplicity Nauk norm normal perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero