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 2300
... dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have Ep ; T + P ) ( I — E , ) = 0 if μ is not one of ...
... dimensional range for all p . Thus , by Lemma VII.6.7 , I — E , has finite dimensional range for all sufficiently large p . Since E is a count- ably additive spectral resolution , we have Ep ; T + P ) ( I — E , ) = 0 if μ is not one of ...
Page 2485
... dimensional range . 13 H , ß , ß Let S , B ( S ) , y , B , Ay , s , and A be as in Exercise 11 . ( a ) Show that if ... dimensional , then the range of IT ( ) has a finite dimensional orthocomplement . 14 Let S be a Hilbert space , R the ...
... dimensional range . 13 H , ß , ß Let S , B ( S ) , y , B , Ay , s , and A be as in Exercise 11 . ( a ) Show that if ... dimensional , then the range of IT ( ) has a finite dimensional orthocomplement . 14 Let S be a Hilbert space , R the ...
Page 2487
... dimensional complement , such that W ( H + T ) ƒ = HWf for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that Σac ( H + T ) has a finite dimensional complement , so ...
... dimensional complement , such that W ( H + T ) ƒ = HWf for all ƒ in the domain of H. ( Hint : Use Exercise 14 , and induction on the dimension of the range of T. ) ( b ) Show that Σac ( H + T ) has a finite dimensional complement , so ...
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