Linear Operators: Spectral operators |
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Page 2393
... real axis ; moreover , each point in Z is a pole of the resolvent of T and a zero of the function A ( A ) . Since A ( λ ) ~ 1 or A ( λ ) ~ μ ( A ) as → ∞ , Z is a bounded set . More- | X | over , since A * ( X ) ‡ 0 , A ̄ ( X ) ÷ 0 ...
... real axis ; moreover , each point in Z is a pole of the resolvent of T and a zero of the function A ( A ) . Since A ( λ ) ~ 1 or A ( λ ) ~ μ ( A ) as → ∞ , Z is a bounded set . More- | X | over , since A * ( X ) ‡ 0 , A ̄ ( X ) ÷ 0 ...
Page 2419
... real numbers , with y > 0 and 1 > ẞ > 0 . Let X be a B - space . Let A be an X - valued function defined on the real axis , and suppose that || A || y . < ∞ . Then : .B ( a ) The improper integral ( 3 ) ( TA ) ( 8 ) = + ∞ A ( o ) 00 A ...
... real numbers , with y > 0 and 1 > ẞ > 0 . Let X be a B - space . Let A be an X - valued function defined on the real axis , and suppose that || A || y . < ∞ . Then : .B ( a ) The improper integral ( 3 ) ( TA ) ( 8 ) = + ∞ A ( o ) 00 A ...
Page 2455
... real axis , then F ( H2 ) Σ ( H1 , H2 ) ≤ Σ ( H1 , H2 ) and ( 4 ) U ( H1 , H2 ) F ( H2 ) x = F ( H1 ) U ( H1 , H2 ) x , χεΣ ( H1 , H2 ) . ( c ) Let D ( H ) be the domain of H , i = 1 , 2. The restrictions H1 | ( Σ ( H2 , H1 ) ~ D ( H1 ) ...
... real axis , then F ( H2 ) Σ ( H1 , H2 ) ≤ Σ ( H1 , H2 ) and ( 4 ) U ( H1 , H2 ) F ( H2 ) x = F ( H1 ) U ( H1 , H2 ) x , χεΣ ( H1 , H2 ) . ( c ) Let D ( H ) be the domain of H , i = 1 , 2. The restrictions H1 | ( Σ ( H2 , H1 ) ~ D ( H1 ) ...
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