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 |
Introduction | 1927 |
Relations Between a Spectral Operator and Its Scalar | 1950 |
Copyright | |
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Common terms and phrases
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