Linear Operators: Spectral operators |
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Page 2187
... measurable function f may be defined as the inte- gral of a bounded E - measurable function which coincides with f , E - almost everywhere on 4. It should also be noted that the space of all E - essentially bounded E - measurable functions ...
... measurable function f may be defined as the inte- gral of a bounded E - measurable function which coincides with f , E - almost everywhere on 4. It should also be noted that the space of all E - essentially bounded E - measurable functions ...
Page 2404
... measurable function . For each number p such that 1≤p≤∞ , define p ' by ( p ' ) − 1 + p ̄1 = 1. Put ( 7 ) and ( 8 ) - 1 -1 1 / p { 4 } , = { ↓ ̧ { √_ | A ( s , t ) \ " ' μ ( dt ) } ' " ' " ' μ ( ds ) } ) } " , 2≤p < 00 , S { A } ...
... measurable function . For each number p such that 1≤p≤∞ , define p ' by ( p ' ) − 1 + p ̄1 = 1. Put ( 7 ) and ( 8 ) - 1 -1 1 / p { 4 } , = { ↓ ̧ { √_ | A ( s , t ) \ " ' μ ( dt ) } ' " ' " ' μ ( ds ) } ) } " , 2≤p < 00 , S { A } ...
Page 2410
... measurable function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || sup A ( z , z ' ) < ∞ , = 2,2'ED and let ( A ) be the integral operator defined by the equation ( 36 ) ...
... measurable function defined in D x D , with values in the space B ( X ) of all bounded operators in X. Suppose that ( 35 ) || A || sup A ( z , z ' ) < ∞ , = 2,2'ED and let ( A ) be the integral operator defined by the equation ( 36 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero