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 |
From inside the book
Results 1-3 of 69
Page 2017
... inequality ( i ) of Theorem 6 is 82-822 + 2 | 8182 | 2 - { ( s2 — s2 ) 2 + 16s181 } 1 / 2 which is bounded on all of R " . Thus Ag has a resolution of the identity . Furthermore , the set S1 is the null set { s | s1 = 82 = 0 } , so that ...
... inequality ( i ) of Theorem 6 is 82-822 + 2 | 8182 | 2 - { ( s2 — s2 ) 2 + 16s181 } 1 / 2 which is bounded on all of R " . Thus Ag has a resolution of the identity . Furthermore , the set S1 is the null set { s | s1 = 82 = 0 } , so that ...
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 ) | fe EB ( A , S ) } is a B - algebra . 1 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 ) | fe EB ( A , S ) } is a B - algebra . 1 To complete the proof of the theorem it only ...
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 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
22 other sections not shown
Other editions - View all
Common terms and phrases
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 inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ 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