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 2017
... inequality ( i ) of Theorem 6 is | 82 — 822 +28182 | 2 { ( s } − s2 ) * + 16s † s1⁄2 } 1 / 2 - which is bounded on all of R " . Thus Ag has a resolution of the identity . Furthermore , the set 1 is the null set { s | s1 = s2 = 0 } , so ...
... inequality ( i ) of Theorem 6 is | 82 — 822 +28182 | 2 { ( s } − s2 ) * + 16s † s1⁄2 } 1 / 2 - which is bounded on all of R " . Thus Ag has a resolution of the identity . Furthermore , the set 1 is the null set { s | s1 = s2 = 0 } , so ...
Page 2190
... inequality of the theorem . From this inequality it is evident that the homomorphism f → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € 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 f → S ( ƒ ) is an isomorphism and that the algebra { S ( ƒ ) | ƒ € EB ( A , S ) } is a B - algebra . To complete the proof of the theorem it only ...
Page 2399
... inequality we have 00 ( 4 1/2 du K2 2 ∞ dμ 。( 1 + μ ) 2 ) L1 / 2 \ f \ 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 00 ( 4 1/2 du K2 2 ∞ dμ 。( 1 + μ ) 2 ) L1 / 2 \ f \ 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 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
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 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