Linear Operators, Part 2 |
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Page 2169
... continuous functions . To see that it is a homomorphism on the algebra of 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 ) ...
... continuous functions . To see that it is a homomorphism on the algebra of 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 ) ...
Page 2456
... continuous function vanishing outside a compact subset of the real axis . Next let F be the characteristic function of an interval of the real axis . Using Theorem XII.2.6 , it follows that we can find a sequence Fr of continuous functions ...
... continuous function vanishing outside a compact subset of the real axis . Next let F be the characteristic function of an interval of the real axis . Using Theorem XII.2.6 , it follows that we can find a sequence Fr of continuous functions ...
Page 2477
... continuous function F defined on R and vanishing ato . Since every bounded continuous function F defined on R is the limit of a uniformly bounded sequence of continuous functions Fn , each vanishing ato , it follows by Theorem XII.2.6 ...
... continuous function F defined on R and vanishing ato . Since every bounded continuous function F defined on R is the limit of a uniformly bounded sequence of continuous functions Fn , each vanishing ato , it follows by Theorem XII.2.6 ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function 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 eigenvalues elements equation exists finite number follows from Lemma 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