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 61
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 2409
... apply Theorem 1 , to find that if A € A , and if || A || is sufficiently small , then the operator T and the ... applies not only to spaces of complex valued functions but also to spaces of X - valued functions , all the above arguments ...
... apply Theorem 1 , to find that if A € A , and if || A || is sufficiently small , then the operator T and the ... applies not only to spaces of complex valued functions but also to spaces of X - valued functions , all the above arguments ...
Page 2434
... Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate " diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may apply Theorem 21 to analyze a variety of operators . The ...
... Applying Theorem 8 and Corollary 9 , the present theorem follows at once . Q.E.D. By using appropriate " diagonalizing " transformations ( cf. Theorem XII.3.16 ) , we may apply Theorem 21 to analyze a variety of operators . The ...
Contents
SPECTRAL OPERATORS | 1924 |
The Resolvent of a Spectral Operator | 1935 |
An Operational Calculus for Bounded Spectral | 1941 |
Copyright | |
23 other sections not shown
Other editions - View all
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