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 H and the bounded normal operators in H ? 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 H and the bounded normal operators in H ? The central result in this direction is a theorem of Wermer which states that every scalar type ...
Page 1947
... ... , k , are all self adjoint . Thus the operators are normal . = -1 BS , B - 1 = √ λBE , ̧ ( 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.
... ... , k , are all self adjoint . Thus the operators are normal . = -1 BS , B - 1 = √ λBE , ̧ ( 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 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