Linear Operators: Spectral operators |
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Page 2400
... similar operators , that is , that there exists a bounded linear operator U with bounded inverse , such that T + KU - 1TU . To verify this conjecture in any particular case , we must solve the linear operator equation U ( TK ) TU for ...
... similar operators , that is , that there exists a bounded linear operator U with bounded inverse , such that T + KU - 1TU . To verify this conjecture in any particular case , we must solve the linear operator equation U ( TK ) TU for ...
Page 2413
... similar whenever || A || < ɛ . Q.E.D. Theorem 1 and its corollaries are readily generalized to apply to unbounded ... similar to T. ( 52 ) PROOF . By Lemma VII.3.4 , the equation B ( B , A1 ) = A1 has a solution BA , whose norm , by this ...
... similar whenever || A || < ɛ . Q.E.D. Theorem 1 and its corollaries are readily generalized to apply to unbounded ... similar to T. ( 52 ) PROOF . By Lemma VII.3.4 , the equation B ( B , A1 ) = A1 has a solution BA , whose norm , by this ...
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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 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