## Linear Operators: Spectral operators |

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Page 1955

We shall be concerned with the fine structure of the

We shall be concerned with the fine structure of the

**spectrum**, and the spectral points of an operator in X will be classified , as they were in Hilbert space , according to the following definition . DEFINITION .Page 2507

uniformly bounded by a constant K in the neighborhood of the

uniformly bounded by a constant K in the neighborhood of the

**spectrum**of H , while the integrals SA ( ( 1 + i € ) 1 – H , ) - 10/2 dx and S \ B * ( ( A + ie ) I – H , ) - 1/2 dx are bounded as ĉ → 0 . In this case , and under the ...Page 2591

... into real and imaginary examples of , XX.1.12 ( 2396 ) , XX.1.14 ( 2399 ) in locally convex spaces , XV.16 ( 2091 ) Spectral resolution , definition of , XV.2.2 ( 1930 ) Spectral set for an operator , XV.2 ( 1930 )

... into real and imaginary examples of , XX.1.12 ( 2396 ) , XX.1.14 ( 2399 ) in locally convex spaces , XV.16 ( 2091 ) Spectral resolution , definition of , XV.2.2 ( 1930 ) Spectral set for an operator , XV.2 ( 1930 )

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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