Linear Operators, Part 2 |
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Results 1-3 of 96
Page 1979
... shows that condition ( i ) of the theorem is satisfied . Q.E.D. 8 COROLLARY . Every operator A in XP is the strong ... shows that A is a spectral operator . Now since it follows that e ( S ) x → → x for every x in H and thus that Ex ...
... shows that condition ( i ) of the theorem is satisfied . Q.E.D. 8 COROLLARY . Every operator A in XP is the strong ... shows that A is a spectral operator . Now since it follows that e ( S ) x → → x for every x in H and thus that Ex ...
Page 2169
... shows that ( vi ) holds for every bounded Borel function f and every continuous function g . A repetition of this argument shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) ...
... shows that ( vi ) holds for every bounded Borel function f and every continuous function g . A repetition of this argument shows that it also holds if ƒ and g are both bounded Borel functions . Thus the operators f ( T ) and g ( T ) ...
Page 2170
... shows that - | ( αI — T ) x | 2 = | I ( α ) x | 2 + | ( R ( a ) I − T ) x | 2 ≥ | J ( a ) | 2 | x | 2 , so that | x | ≤ | ( αI - − T ) x | ( α ) | 1 This shows that ( xIT ) -1 exists as a bounded operator , from which it readily ...
... shows that - | ( αI — T ) x | 2 = | I ( α ) x | 2 + | ( R ( a ) I − T ) x | 2 ≥ | J ( a ) | 2 | x | 2 , so that | x | ≤ | ( αI - − T ) x | ( α ) | 1 This shows that ( xIT ) -1 exists as a bounded operator , from which it readily ...
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