Linear Operators: Spectral operators |
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Page 1945
... Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space 5 and the bounded normal operators in $ ? The central result in this direction is a theorem of Wermer which states that every scalar type ...
... Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space 5 and the bounded normal operators in $ ? The central result in this direction is a theorem of Wermer which states that every scalar type ...
Page 1947
... , are all self adjoint . Thus the operators are normal . 1 BS , B - 1 = \ BE1 ( dλ ) B - 1 , Q.E.D. i = 1 , ... , k , 5 COROLLARY . The sum and the product of two XV.6.2 1947 BOUNDED SPECTRAL OPERATORS IN HILBERT SPACE.
... , are all self adjoint . Thus the operators are normal . 1 BS , B - 1 = \ BE1 ( dλ ) B - 1 , Q.E.D. i = 1 , ... , k , 5 COROLLARY . The sum and the product of two XV.6.2 1947 BOUNDED SPECTRAL OPERATORS IN HILBERT SPACE.
Page 2169
... Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem asserting that a bounded self adjoint operator in ...
... Hilbert Space It is the purpose of this section to show how the theory of spectral operators may be applied to yield the classical spectral theorem in Hilbert space , that is , the theorem asserting that a bounded self adjoint operator in ...
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