Linear Operators: Spectral operators |
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Page 1989
... spectral measure in H , and thus , since F is unitary , the measure e ( o ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
... spectral measure in H , and thus , since F is unitary , the measure e ( o ) , σ € Σ , is a spectral measure with these same properties . We also have e ( o ) = 0 if and only if o has Lebesgue measure zero so that the notions of e ...
Page 2107
... spectral ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of ... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G ...
... spectral ( respectively , scalar type ) operator , then T is spectral ( respectively , scalar type ) . A number of ... measure μ on X to A we mean a mapping 8 → μ ( S ) from the Baire field ( the o - field generated by the compact G ...
Page 2110
... measure space and denote L2 = L , ( S , E , μ ) . Let 1≤r≤s + co and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and TTL , is spectral , then its resolution of the identity is EL ...
... measure space and denote L2 = L , ( S , E , μ ) . Let 1≤r≤s + co and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and TTL , is spectral , then its resolution of the identity is EL ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero