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 2005
... similar to normal operators . Thus both of the operators in ( 57 ) are scalar type operators , and for any a and b in 2 , they are similar to normal operators . In the case of the operators ( 55 ) and ( 58 ) the situation is somewhat ...
... similar to normal operators . Thus both of the operators in ( 57 ) are scalar type operators , and for any a and b in 2 , they are similar to normal operators . In the case of the operators ( 55 ) and ( 58 ) the situation is somewhat ...
Page 2400
... Similar Operators In the present section we shall begin our discussion of an elegant method , due to K. O. Friedrichs , which makes it possible to show , in a variety of cases , that an operator is spectral , and even much more . The ...
... Similar Operators In the present section we shall begin our discussion of an elegant method , due to K. O. Friedrichs , which makes it possible to show , in a variety of cases , that an operator is spectral , and even much more . The ...
Page 2447
... similar to J , so that G is similar to cJ . Q.E.D. 3. The Friedrichs ' Method for the Discrete Spectrum The XX.2.24 2447 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS.
... similar to J , so that G is similar to cJ . Q.E.D. 3. The Friedrichs ' Method for the Discrete Spectrum The XX.2.24 2447 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS.
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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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