Linear Operators: Spectral operators |
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Page 2127
... non - zero real roots , then we can write L2 ( R * ) = M⇒N where M corresponds to the continuous spectrum of L , and N corresponds to the point spectrum of L. If p satisfies the condition [ * ® ea3p ( x ) dx < + ∞ for some ɛ > 0 ...
... non - zero real roots , then we can write L2 ( R * ) = M⇒N where M corresponds to the continuous spectrum of L , and N corresponds to the point spectrum of L. If p satisfies the condition [ * ® ea3p ( x ) dx < + ∞ for some ɛ > 0 ...
Page 2256
... non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ( a ) and ( b ) are satisfied . Since σ ( T ) is totally disconnected , there exists a complex number λ & σ ( T ) ...
... non - zero x in X satisfies the equation E ( o ) x = 0 for every compact spectral set o of T. 1 PROOF . Suppose first that ( a ) and ( b ) are satisfied . Since σ ( T ) is totally disconnected , there exists a complex number λ & σ ( T ) ...
Page 2343
... non - vanishing terms . Thus our 2v × 2v determinant may be expressed as P1P2Q1Q2 , where P1 and P2 are the v × v ... zero , whereas the constant c , of formula ( 13 ) is zero . Consequently , Hypothesis 1 is satisfied and the constant ẞ ...
... non - vanishing terms . Thus our 2v × 2v determinant may be expressed as P1P2Q1Q2 , where P1 and P2 are the v × v ... zero , whereas the constant c , of formula ( 13 ) is zero . Consequently , Hypothesis 1 is satisfied and the constant ẞ ...
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