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 1927
... projection , the above reduc- tion problem stated for I would be : find all projections in X. This problem , while interesting in itself , clearly goes much further than a mere spectral analysis of the operator I. Indeed , since σ ( I ) ...
... projection , the above reduc- tion problem stated for I would be : find all projections in X. This problem , while interesting in itself , clearly goes much further than a mere spectral analysis of the operator I. Indeed , since σ ( I ) ...
Page 2194
... projection operators . The basic result in this direction . is the following theorem of W. G. Bade . THEOREM . Let B be a bounded Boolean algebra of projection operators in a weakly complete B - space X. Then the weakly ( or ...
... projection operators . The basic result in this direction . is the following theorem of W. G. Bade . THEOREM . Let B be a bounded Boolean algebra of projection operators in a weakly complete B - space X. Then the weakly ( or ...
Page 2200
... projection F in S ( B ) is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where y is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E , 2 in B such that E , 2y = y = Fy ...
... projection F in S ( B ) is in B. The proof that F is in B will be made by showing that to each pair ( y , z ) where y is in M FX and z is in N = ( I — F ) X , there can be asso- ciated a projection E , 2 in B such that E , 2y = y = Fy ...
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