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 1945
... Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which states that every ...
... Operators in Hilbert Space What is the relationship between the bounded spectral operators in a Hilbert space H and the bounded normal operators in ? The central result in this direction is a theorem of Wermer which states that every ...
Page 1947
... Hilbert space 5. Then there exists a bounded self adjoint operator B in 5 with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined ... OPERATORS IN HILBERT SPACE.
... Hilbert space 5. Then there exists a bounded self adjoint operator B in 5 with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined ... OPERATORS IN HILBERT SPACE.
Page 2169
... operator . Q.E.D. 6. Self 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 theorem in Hilbert space , that is , the theorem ...
... operator . Q.E.D. 6. Self 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 theorem in Hilbert space , that is , the theorem ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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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 invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian 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