Linear Operators, Part 2 |
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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 ( μIT ) -1ƒ = - - —μ ̄ 1Т - 1 ( μ ̄1I — T - 1 ) - 1ƒ , -1 - μ έ σ ( Τ ) . Since , by this same remark , E ( \ ¡ ̄ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1I — T - 1 ) -1ƒ is analytic ...
... remark following Lemma 2 that ( μIT ) -1ƒ = - - —μ ̄ 1Т - 1 ( μ ̄1I — T - 1 ) - 1ƒ , -1 - μ έ σ ( Τ ) . Since , by this same remark , E ( \ ¡ ̄ ̄1 ; T - 1 ) ƒ = 0 , it follows by Theorem VII.3.20 that ( μ - 1I — T - 1 ) -1ƒ 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 |
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