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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero