Linear Operators: Spectral operators |
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Page 2209
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
... closed algebra generated by B. Q.E.D. 15 COROLLARY . The weakly closed operator algebra generated by a o - complete Boolean algebra B which satisfies the condition of the preceding lemma is the same as the uniformly closed algebra ...
Page 2214
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
... closed operator algebra W ( B ) generated by B is the same as the strongly closed algebra generated by B. Thus every A in W ( B ) is the strong limit of finite linear combinations of elements of B. It follows that A leaves invariant ...
Page 2217
... closed linear manifolds generated by the sets { ExE ¤ B } , { Ex | E ¤ B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
... closed linear manifolds generated by the sets { ExE ¤ B } , { Ex | E ¤ B1 } , respectively . Since B1 is the strong closure of B , each element Ex with E in ... closed operator algebra generated by B ) XVII.3.24 2217 STRONGLY CLOSED ALGEBRAS.
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