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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero