Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Results 1-3 of 18
Page 2320
... evident that by sub- tracting a suitable multiple of B from C , we can pass to an equivalent set of boundary conditions B ( ƒ ) = 0 , ( C — pB ) ( ƒ ) = 0 , where the boundary value C - pB has order less than m at 0. The same ...
... evident that by sub- tracting a suitable multiple of B from C , we can pass to an equivalent set of boundary conditions B ( ƒ ) = 0 , ( C — pB ) ( ƒ ) = 0 , where the boundary value C - pB has order less than m at 0. The same ...
Page 2333
... evident . Q.E.D. As remarked above , it follows immediately from Lemma 7 that the collection of all finite sums of projections Em is bounded . In the same way it follows that the collection of all finite sums of projections Em is ...
... evident . Q.E.D. As remarked above , it follows immediately from Lemma 7 that the collection of all finite sums of projections Em is bounded . In the same way it follows that the collection of all finite sums of projections Em is ...
Page 2394
... evident . The conclusions of ( iv ) relative to B ̄ ( ƒ , g , λ ) may be established in the same way . Q.E.D. To 8 LEMMA . Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oз ( t , μ ) of the equation rσ ...
... evident . The conclusions of ( iv ) relative to B ̄ ( ƒ , g , λ ) may be established in the same way . Q.E.D. To 8 LEMMA . Let the hypotheses of Corollary 2 be satisfied . Then there exists a solution oз ( t , μ ) of the equation rσ ...
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions 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 E₁ 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