Linear Operators: Spectral operators |
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Page 2248
... neighborhood of o ( T ) and a neighborhood of the point at infinity . Suppose that each exceptional point p satisfies E ( p ) = 0 , and that f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a ...
... neighborhood of o ( T ) and a neighborhood of the point at infinity . Suppose that each exceptional point p satisfies E ( p ) = 0 , and that f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a ...
Page 2255
... neighborhood of σ and identically zero in a neighborhood of σ ( T ) — σ . Then ƒ , is analytic in a neighborhood of σ ( T ) and in a neighbor- hood of infinity , so that VII.9.3 f , ( T ) is a well - defined bounded operator . We shall ...
... neighborhood of σ and identically zero in a neighborhood of σ ( T ) — σ . Then ƒ , is analytic in a neighborhood of σ ( T ) and in a neighbor- hood of infinity , so that VII.9.3 f , ( T ) is a well - defined bounded operator . We shall ...
Page 2256
... neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point of σ and no point of σ ( T ) — σ . It is clear ...
... neighborhood of infinity , C1 being oriented in the customary positive sense of complex variable theory . The curves C of the present lemma bound a finite domain D containing every point of σ and no point of σ ( T ) — σ . It is clear ...
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