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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Results 1-3 of 93
Page 1979
... shows that condition ( i ) of the theorem is satisfied . 8 COROLLARY . Every operator A in of spectral operators ... shows that A is a spectral operator . Now since it follows that e ( S ) x- → → x for every x in 5 and thus that Ex ...
... shows that condition ( i ) of the theorem is satisfied . 8 COROLLARY . Every operator A in of spectral operators ... shows that A is a spectral operator . Now since it follows that e ( S ) x- → → x for every x in 5 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 so that | ( αI − T ) x | 2 = | I ( x ) x | 2 + | ( R ( x ) I − T ) x | 2 ≥ | J ( x ) | 2 | x | 2 , - x ≤ ( I_T ) ( α ) | This shows that ( al - T ) -1 exists as a bounded operator , from which it readily follows that ( al ...
... shows that so that | ( αI − T ) x | 2 = | I ( x ) x | 2 + | ( R ( x ) I − T ) x | 2 ≥ | J ( x ) | 2 | x | 2 , - x ≤ ( I_T ) ( α ) | This shows that ( al - T ) -1 exists as a bounded operator , from which it readily follows that ( al ...
Contents
SPECTRAL OPERATORS | 1924 |
The Spectrum of a Spectral Operator | 1955 |
The Algebras A and | 1966 |
Copyright | |
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A₁ Acad adjoint operator algebra of projections Amer analytic arbitrary B-algebra B-space 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 dense differential operator Dokl Doklady Akad eigenvalues elements equation exists formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis ibid identity inequality invariant subspaces inverse Krein L₁ Lemma locally convex spaces multiplicity Nauk SSSR nonselfadjoint norm normal operators operators in Hilbert perturbation Proc PROOF properties prove Pures Appl quasi-nilpotent resolution Russian satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose topology trace class type spectral operator unbounded uniformly bounded vector zero