Linear Operators: Spectral operators |
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Page 2084
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T , ) E ( 0 ) | ≤ dist ( , ) m for § ‡ ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
... complex B - space X which satisfies the growth condition ( * ) in Theorem XV.6.7 , namely K ( * ) | R ( § ; T , ) E ( 0 ) | ≤ dist ( , ) m for § ‡ ō , | § | ≤ | T | + 1. If k is a natural number then there exists a constant M such ...
Page 2171
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
Page 2188
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set Д and let g be a bounded Borel measurable function defined on the complex plane . Then √g ( f ( \ ) ) E ( dλ ) = Sun 9 ( μ ) E ( ƒ ̃ 1 ...
... complex B - space X which is defined and countably additive on a o - field Σ of subsets of a set Д and let g be a bounded Borel measurable function defined on the complex plane . Then √g ( f ( \ ) ) E ( dλ ) = Sun 9 ( μ ) E ( ƒ ̃ 1 ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero