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 2203
... topology of 4. Since σ ( E ) o ( F ) = o ( EF ) , the sets o ( E ) actually form a basis for the topology in 4 ( cf. Theorem IX.2.11 and its proof ) . 1 Consider now a closed set d1 with d≤ 81 ≤e . Each point à in d1 is interior to ...
... topology of 4. Since σ ( E ) o ( F ) = o ( EF ) , the sets o ( E ) actually form a basis for the topology in 4 ( cf. Theorem IX.2.11 and its proof ) . 1 Consider now a closed set d1 with d≤ 81 ≤e . Each point à in d1 is interior to ...
Page 2278
... topology by the manifolds { N ( x * ) | x * € A } . The next lemma establishes the required continuity properties . 23 LEMMA . If E * , F * ɛ C * and F * ≤ E * , then m ( F * ) ≤ m ( E * ) . If { E * } ≤ C * and E * = \ / \ / E * = C ...
... topology by the manifolds { N ( x * ) | x * € A } . The next lemma establishes the required continuity properties . 23 LEMMA . If E * , F * ɛ C * and F * ≤ E * , then m ( F * ) ≤ m ( E * ) . If { E * } ≤ C * and E * = \ / \ / E * = C ...
Page 2281
... topologies and also when X * has its X - topology and Σî = 1 L1 ( A , B , v1 ) has its weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of Theorem 19. Given x * € X * there exist ...
... topologies and also when X * has its X - topology and Σî = 1 L1 ( A , B , v1 ) has its weak topology . PROOF . Most of the proof of this theorem is a straightforward modi- fication of the proof of Theorem 19. Given x * € X * there exist ...
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