Linear Operators: Spectral operators |
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Page 2017
... inequality ( i ) of Theorem 6 holds . Here the set 1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
... inequality ( i ) of Theorem 6 holds . Here the set 1 is void so that A is a scalar type spectral operator to which Theorem 5 applies . Another type of differential operator whose extension is a spectral operator which is not a scalar ...
Page 2190
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) fe EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only remains ...
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) fe EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only remains ...
Page 2221
... inequality gn ( ) ≤ 1 elsewhere ( cf. Theorem I.5.2 ) . Then fg , is continuous so that , by Corollary 2 , lim f ( Ta ) 9n ( Ta ) x = ƒ ( T ) gn ( T ) x , α x = x . Similarly lim 。 9n ( Ta ) = 9n ( T ) in the strong operator topology ...
... inequality gn ( ) ≤ 1 elsewhere ( cf. Theorem I.5.2 ) . Then fg , is continuous so that , by Corollary 2 , lim f ( Ta ) 9n ( Ta ) x = ƒ ( T ) gn ( T ) x , α x = x . Similarly lim 。 9n ( Ta ) = 9n ( T ) in the strong operator topology ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero