Linear Operators: Spectral operators |
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Page 2092
... equivalent ; the general notion extends this case . ) The relation of being quasi - nilpotent equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) o ( T ) = o ( U ) , ( ii ) T has ...
... equivalent ; the general notion extends this case . ) The relation of being quasi - nilpotent equivalent is indeed an equivalence relation and , when T and U are quasi - nilpotent equivalent , then ( i ) o ( T ) = o ( U ) , ( ii ) T has ...
Page 2105
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒƒ ( s ) E ( ds ) || = sup | ƒ ( 8 ) ...
... equivalent to | · | and relative to which all the operators E ( S ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒƒ ( s ) E ( ds ) || = sup | ƒ ( 8 ) ...
Page 2115
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
... equivalent , then U is a spectral operator . Moreover , if T and U are spectral , then they are quasi - nilpotent equivalent if and only if they have the same resolution of the identity , and if and only if the single condition : lim ...
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