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 + K = U¬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 + K = U¬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 algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero