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 2082
... exercise , let x , xo , and σ 。 be chosen so that x * E ( oo ) x 。 0 and let g be the Radon - Nikodým deriva- tive of x * E ( ) x , with respect to μ . There is a subset o1 of oo on which g is bounded away from zero and we let = 1 / g ...
... exercise , let x , xo , and σ 。 be chosen so that x * E ( oo ) x 。 0 and let g be the Radon - Nikodým deriva- tive of x * E ( ) x , with respect to μ . There is a subset o1 of oo on which g is bounded away from zero and we let = 1 / g ...
Page 2480
... exercises in the immediately following section . 5. Exercises 1 2 1 Let H1 and H2 be unbounded self adjoint operators in ... exercise , if 7 denotes a formal partial differential operator defined in the Euclidean space E " , then T1 ( 7 ) ...
... exercises in the immediately following section . 5. Exercises 1 2 1 Let H1 and H2 be unbounded self adjoint operators in ... exercise , if 7 denotes a formal partial differential operator defined in the Euclidean space E " , then T1 ( 7 ) ...
Page 2489
... exercise . ) 19 Let H be a self adjoint operator in Hilbert space . Let V be an operator of trace class , and put H1 Let weΣac ( H ) and || w || , < ∞ ас H ( a ) Show that the limit = t H + V. Put U1 = exp ( itH1 ) exp ( —itH ) . ( cf ...
... exercise . ) 19 Let H be a self adjoint operator in Hilbert space . Let V be an operator of trace class , and put H1 Let weΣac ( H ) and || w || , < ∞ ас H ( a ) Show that the limit = t H + V. Put U1 = exp ( itH1 ) exp ( —itH ) . ( cf ...
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