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 2169
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
... bounded Borel functions , note that for a fixed continuous function g the set of all bounded Borel functions ƒ for which ( vi ) ( fg ) ( T ) = ƒ ( T ) g ( T ) , includes all continuous functions . Furthermore , if the equation ( vi ) ...
Page 2252
... bounded case by writing NTS runs into difficulties . The operator N , although easily seen by Lemma 2 to have a ... operator C introduced as an example in the paragraphs of discus- sion preceding Lemma 19 , we see from the discussion ...
... bounded case by writing NTS runs into difficulties . The operator N , although easily seen by Lemma 2 to have a ... operator C introduced as an example in the paragraphs of discus- sion preceding Lemma 19 , we see from the discussion ...
Page 2361
... bounded domains covering the whole complex plane , and suppose that lim - min2e U1 | 2 | ∞ . Let V be the boundary of U1 . Let 0 ≤ v < 1 , and = put μι = max - λενί , μεσ ( Τ ) Let λoo ( T ) , and let P be an operator such that P ( T ...
... bounded domains covering the whole complex plane , and suppose that lim - min2e U1 | 2 | ∞ . Let V be the boundary of U1 . Let 0 ≤ v < 1 , and = put μι = max - λενί , μεσ ( Τ ) Let λoo ( T ) , and let P be an operator such that P ( T ...
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