## Linear Operators: Spectral operators |

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T = T ( f ) in the sense of

T = T ( f ) in the sense of

**Definition**10 , where f ( z ) = , then T is said to be an unbounded spectral operator of scalar type . The projection valued measure E is said to be the resolution of the identity for T. 13 LEMMA .Page 2590

Restriction of a spectral operator , spectrum of , XV.8.5 ( 1956 ) Quantum mechanical three - body problem , XX.6 ( 2501 ) , ( 2507 ) Quantum theory of fields , XX.6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

Restriction of a spectral operator , spectrum of , XV.8.5 ( 1956 ) Quantum mechanical three - body problem , XX.6 ( 2501 ) , ( 2507 ) Quantum theory of fields , XX.6 ( 2501 ) , ( 2507 ) Quasi - nilpotent operator ,

**definition**of ...Page 2591

countably additive , XV.2 ( 1930 ) , XV.2.3 ( 1930 ) , XV.2.4 ( 1931 )

countably additive , XV.2 ( 1930 ) , XV.2.3 ( 1930 ) , XV.2.4 ( 1931 )

**definition**of , XV.2.1 ( 1929 ) integral with respect to , XV.2 ( 1929 ) Spectral operator , adjoint of , XVI.4.6 ( 2148 ) , XVI.5.16 ( 2162 ) canonical reduction of ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 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