Linear Operators: Spectral operators |
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Page 1935
... complex numbers is a closed linear manifold in X. 7 COROLLARY . Let T be a spectral operator and A a bounded linear transformation which commutes with T. Then A commutes with every resolu- tion of the identity for T. Moreover o ( Ax ) ...
... complex numbers is a closed linear manifold in X. 7 COROLLARY . Let T be a spectral operator and A a bounded linear transformation which commutes with T. Then A commutes with every resolu- tion of the identity for T. Moreover o ( Ax ) ...
Page 1955
... complex numbers À for which XI - A is not one - to - one . The continuous spectrum of A is the set σ ( A ) of complex numbers À for which I — A is one - to - one and has a dense range which is not equal to X. The residual spectrum of A ...
... complex numbers À for which XI - A is not one - to - one . The continuous spectrum of A is the set σ ( A ) of complex numbers À for which I — A is one - to - one and has a dense range which is not equal to X. The residual spectrum of A ...
Page 2171
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
... complex B - space X. For each x in X the symbol [ x ] will be used for the closed linear manifold determined by all the vectors R ( § ; T ) x with έ in p ( T ) . If σ is a closed set of complex numbers , the symbol M ( o ) will denote ...
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