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 A , 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 A , they are similar to normal operators . In the case of the operators ( 55 ) and ( 58 ) the situation is somewhat ...
Page 2401
... similar if there exists a bounded operator U in Y with a bounded inverse such that SU - 1TU . Note that Definition 2 ... similar . PROOF . Using hypothesis ( e ) and Lemma VII.3.4 XX.2.2 2401 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS.
... similar if there exists a bounded operator U in Y with a bounded inverse such that SU - 1TU . Note that Definition 2 ... similar . PROOF . Using hypothesis ( e ) and Lemma VII.3.4 XX.2.2 2401 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS.
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 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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