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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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 ( f ) | ƒ e EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
... inequality of the theorem . From this inequality it is evident that the homomorphism ƒ → S ( ƒ ) is an isomorphism and that the algebra { S ( f ) | ƒ e EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
Page 2399
... inequality we have ( 4 - 1/2 00 αμ du ≤ K2 。( 1 + μ ) 2 ) L1 | 2 | S | 2 . The inequality ( 42a ) follows immediately from ( 43 ) and ( 45 ) . Since the inequality ( 42b ) may be deduced in a precisely similar way , the proof of our ...
... inequality we have ( 4 - 1/2 00 αμ du ≤ K2 。( 1 + μ ) 2 ) L1 | 2 | S | 2 . The inequality ( 42a ) follows immediately from ( 43 ) and ( 45 ) . Since the inequality ( 42b ) may be deduced in a precisely similar way , the proof of our ...
Page 2403
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
... inequality for integral operators ( Lemma 5 below ) which is elementary in the sense that it relates only to the norms of the integral kernels involved . We then use this inequality to apply Theorem 1 in an illustrative but somewhat ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero