Linear Operators: Spectral operators |
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Page 2147
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
... linear operator T satisfy conditions ( A ) , ( B ) , and ( C ) . Then , by Theorem 3.11 and Lemma 3 , T is a spectral operator of class ( ( T ) , X * ) with a resolution of the identity which is countably additive in the strong operator ...
Page 2162
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
... linear operator in the B - space X which satisfies conditions ( B ) and ( G ) and let B be the field of Borel sets in the plane . Then the adjoint T * is a spectral operator of class ( B , X ) provided that any one of the conditions ( a ) ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
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