Linear Operators: Spectral operators |
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Page 2133
... remarks , and applications . We remark only that the notion of the index arose in 1921 in connection with the study of certain singular integral equations by F. Noether . In essence , the first stability theorem was proved by Dieudonné ...
... remarks , and applications . We remark only that the notion of the index arose in 1921 in connection with the study of certain singular integral equations by F. Noether . In essence , the first stability theorem was proved by Dieudonné ...
Page 2296
... remark following Lemma 2 that 1 -1 ( μI − T ) - 1ƒ = −μ ̄1T - 1 ( μ ̃1I — T− 1 ) − 1ƒ , μ έ σ ( Τ ) . Since , by this same remark , E ( λ¡ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1I — T - 1 ) -1f is analytic ...
... remark following Lemma 2 that 1 -1 ( μI − T ) - 1ƒ = −μ ̄1T - 1 ( μ ̃1I — T− 1 ) − 1ƒ , μ έ σ ( Τ ) . Since , by this same remark , E ( λ¡ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1I — T - 1 ) -1f is analytic ...
Page 2342
... remark following formula ( 3 ) , it is no loss of generality to assume that the order of B , is m1 , and that m1 ... remark following Regularity Hypothesis 1 , we may then assume without loss of generality that Biff ( i ) ( 0 ) for 1≤i ...
... remark following formula ( 3 ) , it is no loss of generality to assume that the order of B , is m1 , and that m1 ... remark following Regularity Hypothesis 1 , we may then assume without loss of generality that Biff ( i ) ( 0 ) for 1≤i ...
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