Linear Operators, Part 2 |
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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 2400
... similar operators , that is , that there exists a bounded linear operator U with bounded inverse , such that T + K = U - 1TU . To verify this conjecture in any particular case , we must solve the linear operator equation U ( T + K ) ...
... similar operators , that is , that there exists a bounded linear operator U with bounded inverse , such that T + K = U - 1TU . To verify this conjecture in any particular case , we must solve the linear operator equation U ( T + K ) ...
Page 2401
... similar if there exists a bounded operator U in Y with a bounded inverse such that S = U - 1TU . Note that ... similar . PROOF . Using hypothesis ( e ) and Lemma VII.3.4 XX.2.2 2401 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS 3.
... similar if there exists a bounded operator U in Y with a bounded inverse such that S = U - 1TU . Note that ... similar . PROOF . Using hypothesis ( e ) and Lemma VII.3.4 XX.2.2 2401 FRIEDRICHS ' METHOD OF SIMILAR OPERATORS 3.
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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