Linear Operators: Spectral operators |
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Page 1939
... quasi - nilpotent if and only if o ( T ) = { 0 } . PROOF . This follows from Lemma VII.3.4 . Q.E.D. 4 LEMMA . If S and N are bounded commuting operators and if N is quasi - nilpotent , then o ( S + N ) = σ ( S ) . PROOF . This is a ...
... quasi - nilpotent if and only if o ( T ) = { 0 } . PROOF . This follows from Lemma VII.3.4 . Q.E.D. 4 LEMMA . If S and N are bounded commuting operators and if N is quasi - nilpotent , then o ( S + N ) = σ ( S ) . PROOF . This is a ...
Page 2092
... quasi - nilpotent 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 ...
... quasi - nilpotent 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 ...
Page 2252
... quasi - nilpotent restriction to each space E ( o ) X with o bounded , need not be quasi - nilpotent itself . It may be bounded and not quasi - nilpotent , and it may even be unbounded . It is even possible that NS - 1 should fail to be ...
... quasi - nilpotent restriction to each space E ( o ) X with o bounded , need not be quasi - nilpotent itself . It may be bounded and not quasi - nilpotent , and it may even be unbounded . It is even possible that NS - 1 should fail to be ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
Copyright | |
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A₁ adjoint operator 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 operators 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 sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero