Linear Operators: Spectral operators |
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Page 1947
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... , B. 1 - PROOF . For Ee B1 , put F ( E ) = 1 − 2E ...
... adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean algebra determined by the algebras B1 , ... , B. 1 - PROOF . For Ee B1 , put F ( E ) = 1 − 2E ...
Page 2460
... adjoint operator in sing ( H ) , and that H│ ( Σ , ( H ) ~ D ( H ) ) is a densely defined self adjoint operator in Σ , ( H ) ; details are left to the reader . Statement ( c ) of the present lemma follows at once . Finally , to prove ...
... adjoint operator in sing ( H ) , and that H│ ( Σ , ( H ) ~ D ( H ) ) is a densely defined self adjoint operator in Σ , ( H ) ; details are left to the reader . Statement ( c ) of the present lemma follows at once . Finally , to prove ...
Page 2481
... adjoint operator , and that if ƒ = D ( T1 ( V ) ) is a function in its domain , then affär , and a2f / dx , dx , are ... operator , and that , as → ∞ , T1 ( T1 ) ( T1 ( V ) + λI ) −1 converges uniformly to zero . ( c ) Show , under ...
... adjoint operator , and that if ƒ = D ( T1 ( V ) ) is a function in its domain , then affär , and a2f / dx , dx , are ... operator , and that , as → ∞ , T1 ( T1 ) ( T1 ( V ) + λI ) −1 converges uniformly to zero . ( c ) Show , under ...
Contents
SPECTRAL OPERATORS | 1924 |
Spectral Operators | 1925 |
Terminology and Preliminary Notions | 1928 |
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 follows from Theorem 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