Linear Operators: Spectral operators |
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Page 1947
... bounded Boolean algebras of projections in a Hilbert space H. 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 projection for every E in the Boolean ...
... bounded Boolean algebras of projections in a Hilbert space H. 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 projection for every E in the Boolean ...
Page 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
Page 2239
Nelson Dunford, Jacob T. Schwartz. Since fx . is a bounded function , the operator T ( ƒ Xe ) is a bounded operator . If x is in E ( e ) as well as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf. XVII ...
Nelson Dunford, Jacob T. Schwartz. Since fx . is a bounded function , the operator T ( ƒ Xe ) is a bounded operator . If x is in E ( e ) as well as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf. XVII ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 Borel function 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 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