Linear Operators: Spectral operators |
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Page 1939
... quasi - nilpotent if and only if σ ( T ) = { 0 } . PROOF . This follows from Lemma VII.3.4 . Q.E.D. 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 σ ( T ) = { 0 } . PROOF . This follows from Lemma VII.3.4 . Q.E.D. 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 2115
... quasi - nilpotent equivalent , then U is decomposable . Moreover , if T and U are decomposable , then XT ( F ) = X ( F ) for all closed sets F if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator and T ...
... quasi - nilpotent equivalent , then U is decomposable . Moreover , if T and U are decomposable , then XT ( F ) = X ( F ) for all closed sets F if and only if T and U are quasi - nilpotent equivalent . If T is a spectral operator and T ...
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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
22 other sections not shown
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Common terms and phrases
A₁ adjoint operator algebra of projections Amer arbitrary B*-algebra B₁ Boolean algebra Borel sets boundary conditions bounded linear operator bounded operator closed operator Colojoară commuting compact complex numbers complex plane contains converges Corollary countably additive Definition dense differential operator disjoint Doklady Akad E-measurable eigenvalues elements equation equivalent exists Foias follows from Theorem formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math matrix multiplicity norm operators in Hilbert perturbation polynomial PROOF proved quasi-nilpotent resolution restriction Russian S₁ satisfies scalar operator scalar type operator scalar type spectral Section semi-group sequence shows spectral measure spectral operator spectral theory spectrum strong operator topology subset subspace sufficiently type spectral operator unbounded unique vector weakly complete zero