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 2022
... function defined on the spec- trum σ ( A¿ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) = ƒ ( Â ( s ) ) . ( If the roots of the minimal ...
... function defined on the spec- trum σ ( A¿ ) = σ ( Â ) . We simply define the p xp matrix ƒ ( Â ) ( s ) whose elements are measurable functions on RN by the equation ƒ ( Â ) ( s ) = ƒ ( Â ( s ) ) . ( If the roots of the minimal ...
Page 2238
... DEFINITION . Let S be a set , Σ a σ - field of subsets of S , and E a strongly countably additive spectral measure defined on E. Let ƒ be a E - measurable function defined E - almost everywhere on S. Then the operator T ( f ) is defined ...
... DEFINITION . Let S be a set , Σ a σ - field of subsets of S , and E a strongly countably additive spectral measure defined on E. Let ƒ be a E - measurable function defined E - almost everywhere on S. Then the operator T ( f ) is defined ...
Page 2410
... function defined in D × D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || = sup | A ( z , z ' ) | < ∞ , 2,2'ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ( p ( 4 ) ...
... function defined in D × D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || = sup | A ( z , z ' ) | < ∞ , 2,2'ED and let ( 4 ) be the integral operator defined by the equation ( 36 ) ( p ( 4 ) ...
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