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
... Hilbert space $ . Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint ... OPERATORS IN HILBERT SPACE Bounded Spectral Operators in Hilbert Space 1925.
... Hilbert space $ . Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint ... OPERATORS IN HILBERT SPACE Bounded Spectral Operators in Hilbert Space 1925.
Page 1948
... operators in Hilbert space are also spectral operators . The proof of this corollary will use the following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space with A normal . Then if B commutes with A , it commutes with ...
... operators in Hilbert space are also spectral operators . The proof of this corollary will use the following lemma . 6 LEMMA . Let A and B be bounded operators in Hilbert space with A normal . Then if B commutes with A , it commutes with ...
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 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
The Algebras and | 1967 |
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 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