Linear Operators: Spectral operators |
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Page 1989
... spectral measure in 5 , and thus , since F is unitary , the measure e ( σ ) , 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 5 , and thus , since F is unitary , the measure e ( σ ) , 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 μ ) . = L , ( S , E , μ ) . Let 1 ≤r≤8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
... measure space and denote L2 μ ) . = L , ( S , E , μ ) . Let 1 ≤r≤8 ≤ + ∞ and let T be a spectral opera- tor on L , with resolution of the identity E. If T leaves L , invariant and T , TL , is spectral , then its resolution of the ...
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