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