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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero