Linear Operators, Part 2 |
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Page 2087
... strongly continuous semi - group S ( t ) , t≥ 0 , of bounded linear operators in H and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for ( in the half plane R ( Ž ) > 0 . For every ( 0 ) in Ho there is one ...
... strongly continuous semi - group S ( t ) , t≥ 0 , of bounded linear operators in H and S ( t ) has a strongly analytic extension to a semi - group S ( ) defined for ( in the half plane R ( Ž ) > 0 . For every ( 0 ) in Ho there is one ...
Page 2194
... Strongly Closed Algebras and Complete Boolean Algebras In this section an attempt will be made to characterize the strong closure of a commutative algebra of spectral operators . It has been observed ( cf. VI.1.5 ) that a convex set in ...
... Strongly Closed Algebras and Complete Boolean Algebras In this section an attempt will be made to characterize the strong closure of a commutative algebra of spectral operators . It has been observed ( cf. VI.1.5 ) that a convex set in ...
Page 2220
... strongly convergent generalized sequences is itself a strongly convergent generalized sequence , we see that r ( Ta ) → r ( T ) strongly . Now , from Theorem 2.10 , \ r ( T ) | = | √ , r ( \ ) E , ( d ) ) | ≤ 4M sup | r ( 5 ) , and ...
... strongly convergent generalized sequences is itself a strongly convergent generalized sequence , we see that r ( Ta ) → r ( T ) strongly . Now , from Theorem 2.10 , \ r ( T ) | = | √ , r ( \ ) E , ( d ) ) | ≤ 4M sup | r ( 5 ) , and ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
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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 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