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 , ... , B. - - PROOF . For Ee B1 , put F ( E ) = I - 2E ...
... 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 , ... , B. - - PROOF . For Ee B1 , put F ( E ) = I - 2E ...
Page 2106
... adjoint Abelian if A * q = ¢ A ( equivalently , if ( Ax ) * = A * x * for all xe X ) . If A is adjoint Abelian , then o ( A ) is real and A2n 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 xe X ) . If A is adjoint Abelian , then o ( A ) is real and A2n 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 ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert Space Exercises 2149.
... 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 ... ADJOINT OPERATORS IN HILBERT SPACE Self Adjoint Operators in Hilbert Space Exercises 2149.
Contents
SPECTRAL OPERATORS | 1924 |
An Operational Calculus for Bounded Spectral | 1941 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR norm normal operators operators in Hilbert perturbation polynomial Proc PROOF properties prove Pure Appl quasi-nilpotent resolution Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero