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 ) σ ( 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 ) σ ( T ) = o ( U ) , ( ii ) T has ...
Page 2105
... equivalent to || and relative to which all the operators E ( 8 ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( s ) E ( ds ) || = sup | ƒ ( 8 ) ...
... equivalent to || and relative to which all the operators E ( 8 ) become Hermitian . It follows from this and Berkson [ 5 ; p.3 ] that if f is continuous on the compact support K of E , then || ƒ ƒ ( 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 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ algebra Amer analytic applications arbitrary B-space Banach Banach space Boolean algebra Borel sets boundary bounded Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator Doklady Akad elements equation equivalent established example exists extension finite follows formula function given gives H₁ Hence Hilbert space hypothesis identity integral invariant inverse Lemma limit linear operators Math multiplicity Nauk SSSR norm normal perturbation plane positive preceding present problem Proc projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero