Linear Operators: Spectral operators |
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Page 1930
... resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , σ ( T¿ ) ≤ 8 , δε Σ . δ Here we have used , and shall continue to use , the symbol T , for the restriction TX of T to the manifold X ...
... resolution of the identity ( or a spectral resolution ) for the operator T if E ( S ) T = TE ( S ) , σ ( T¿ ) ≤ 8 , δε Σ . δ Here we have used , and shall continue to use , the symbol T , for the restriction TX of T to the manifold X ...
Page 2094
... resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where ** , then it has a unique resolution of the identity of class ( T ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has ...
... resolution of the identity of class ( X ) ; moreover , if T * is spectral of class ( I ) where ** , then it has a unique resolution of the identity of class ( T ) . If X * is weakly complete and T is spectral of class ( Ã ) , then T has ...
Page 2242
... resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the sense ...
... resolution of the identity for T. 13 LEMMA . An unbounded spectral operator of scalar type in the sense of Definition 12 is a spectral operator in the sense of Definition 1. Moreover , the resolution of the identity for T in the sense ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero