Linear Operators, Part 2 |
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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 ΧΙ A is not one - to - one . The continuous spectrum of A is the set o¿ ( A ) of complex numbers À for which λ — 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 ΧΙ A is not one - to - one . The continuous spectrum of A is the set o¿ ( A ) of complex numbers À for which λ — 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 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero