Linear Operators: Spectral operators |
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Page 2179
... algebra of scalar type operators which is equivalent to an algebra of continuous functions . = 1 LEMMA . The uniformly closed algebra of operators generated by a ... B - ALGEBRAS The Structure of Commutative B-Algebras Spectral Operators.
... algebra of scalar type operators which is equivalent to an algebra of continuous functions . = 1 LEMMA . The uniformly closed algebra of operators generated by a ... B - ALGEBRAS The Structure of Commutative B-Algebras Spectral Operators.
Page 2183
... algebra generated by the projections in its resolution of the identity ( cf. Definition XV.4.1 ) , B27 . It will be shown below that B is a full algebra , from which it follows that B A ( 7 ) . It will also be shown that P ... B - ALGEBRAS.
... algebra generated by the projections in its resolution of the identity ( cf. Definition XV.4.1 ) , B27 . It will be shown below that B is a full algebra , from which it follows that B A ( 7 ) . It will also be shown that P ... B - ALGEBRAS.
Page 2193
... B are all contained in a bounded Boolean algebra B of projections , and thus the desired decomposition of A follows from Theorem 3. The final assertion follows from Corollary 14. Q.E.D. The preceding corollary is not true if the Hilbert ...
... B are all contained in a bounded Boolean algebra B of projections , and thus the desired decomposition of A follows from Theorem 3. The final assertion follows from Corollary 14. Q.E.D. The preceding corollary is not true if the Hilbert ...
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