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 in 5 and a point t in RN the translate q , in H , defined as Pt ( s ) = p ( s − t ) , when regarded as a map t → 9 , of RN into H , is ...
... vector valued function , or a principal value integral of a vector valued function . For a given in 5 and a point t in RN the translate q , in H , defined as Pt ( s ) = p ( s − t ) , when regarded as a map t → 9 , of RN into H , 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 ...
... 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 ...
Page 2266
... vector x is sp { Ex | E 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 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 |
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