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 1915
... apply , has a direct short path to these problems ; namely , Theorem XVI.5.19 , its unbounded counterpart found in ... application to the spectral analysis of PREFACE xi.
... apply , has a direct short path to these problems ; namely , Theorem XVI.5.19 , its unbounded counterpart found in ... application to the spectral analysis of PREFACE xi.
Page 2403
... apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ...
... apply Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ...
Page 2418
... apply Theorem 8 and Corollary 9 , and the conclusion of the present theorem follows immediately . Q.E.D. As the ... application of Theorems 1 and 2418 SPECTRAL OPERATORS WITH CONTINUOUS SPECTRA XX.2.10.
... apply Theorem 8 and Corollary 9 , and the conclusion of the present theorem follows immediately . Q.E.D. As the ... application of Theorems 1 and 2418 SPECTRAL OPERATORS WITH CONTINUOUS SPECTRA XX.2.10.
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 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