Linear Operators: Spectral operators |
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Page 2249
... Theorem 9 ( v ) that ( 1 / ƒ ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
... Theorem 9 ( v ) that ( 1 / ƒ ) ( A ) is bounded . This proves the first two assertions of the present theorem , and also the inclusion o ( ƒ ( T ) ) ≤ ƒ ( o ( T ) ) , which is part of the final assertion of the present theorem . Since ...
Page 2403
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
... Theorem 1 in an illustrative but somewhat artificial setting , essentially to multiplication operators whose spectral measures are absolutely continuous with respect to two - dimensional Lebesgue measure . A first application ( Theorem ...
Page 2418
... theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
... theorem ( III.11.14 ) , the integral ( 75 ) SS141 ( 2 , 2 ) | D | A2 ( z , z ' ) | | zz | f ( z ) dx ' dy ' dx dy exists for almost all z " € D. It follows from ( 65 ) and ( 68 ) , and from Fubini's theorem ( III.11.9 ) , that p ( A1 ) ...
Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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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