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 bounded Boolean algebra of projection operators is a full algebra ...
... 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 bounded Boolean algebra of projection operators is a full algebra ...
Page 2194
... algebra of all operators of the form ƒƒ ( λ ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A , is a full algebra of scalar type spectral operators which is equivalent to EB ( A , Σ ) . It ...
... algebra of all operators of the form ƒƒ ( λ ) E ( dλ ) where ƒ is E - essentially bounded on o ( S ) . It follows from Theorem 10 that A , is a full algebra of scalar type spectral operators which is equivalent to EB ( A , Σ ) . It ...
Page 2214
... 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 every closed linear ...
... 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 every closed linear ...
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