Linear Operators: Spectral operators |
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Page 1990
... vector valued function , or a principal value integral of a vector valued function . For a given o in H and a point t in RN the translate t in H , defined as Pt ( s ) = q ( st ) , when regarded as a map t → q , of RN into 5 , is ...
... vector valued function , or a principal value integral of a vector valued function . For a given o in H and a point t in RN the translate t in H , defined as Pt ( s ) = q ( st ) , when regarded as a map t → q , of RN into 5 , is ...
Page 2160
... vector x in X is the sum of a vector y with ( λ。I — T ) y = 0 and a vector x -y in the closure of ( I − T ) X . Since λo is interior to an interval of constancy relative to T , it is therefore a regular point relative to T. ― Q.E.D. ...
... vector x in X is the sum of a vector y with ( λ。I — T ) y = 0 and a vector x -y in the closure of ( I − T ) X . Since λo is interior to an interval of constancy relative to T , it is therefore a regular point relative to T. ― Q.E.D. ...
Page 2266
... vector x is sp { Ex | E = B } . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying ...
... vector x is sp { Ex | E = B } . A projection E e B will be said to satisfy the countable chain condition if every family of disjoint projections in B bounded by E is at most countable . We shall denote by the set of all Ee B satisfying ...
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