Linear Operators, Part 2 |
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Page 2162
... Theorem 4.5 , to prove the present theorem it suffices to show that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if the points regular relative to T are dense on T 。. Thus Lemmas 12 , 13 , 14 give the ...
... Theorem 4.5 , to prove the present theorem it suffices to show that T has property ( D ) . According to Lemma 10 condition ( D ) will be satisfied if the points regular relative to T are dense on T 。. Thus Lemmas 12 , 13 , 14 give the ...
Page 2403
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) SS 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | If ( z ' ) dx ' dy ' dx dy - D D exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
... theorem ( III.11.14 ) , the integral ( 75 ) SS 141 ( 2 " , 2 ) | | A2 ( z , z ' ) | If ( z ' ) dx ' dy ' dx dy - D D exists for almost all z " e D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
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