Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |
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Page 1947
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , . = - 1 Bk - - - PROOF . For E = B1 , put F ( E ) = I ...
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , . = - 1 Bk - - - PROOF . For E = B1 , put F ( E ) = I ...
Page 2106
... adjoint Abelian if A * q = ¢ A ( equivalently , if ( Ax ) * = A * x * for all x € X ) . If A is adjoint Abelian , then o ( A ) is real and A2 " is Hermitian for n = 1 , 2 , ; however ; A need not be Hermitian , and cI + A need not be ...
... adjoint Abelian if A * q = ¢ A ( equivalently , if ( Ax ) * = A * x * for all x € X ) . If A is adjoint Abelian , then o ( A ) is real and A2 " is Hermitian for n = 1 , 2 , ; however ; A need not be Hermitian , and cI + A need not be ...
Page 2169
... Adjoint Operators 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 ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert Space.
... Adjoint Operators 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 ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert Space.
Contents
SPECTRAL OPERATORS | 1924 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions 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 E₁ 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