Linear Operators: Spectral operators |
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Page 1991
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
... continuous and has its values in a compact set , it is A - measurable and thus integrable . For , in this case , the range of ƒ may be covered with a finite number of open sets G1 , ... , G2 , each having diameter less than a given ...
Page 2066
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
... continuous map of RN into L1 ( XI.3.1 ( f ) ) and since h is continuous ( IX.2.3 ) , the inequality ( 7 ) shows that c ( t ) is continuous in t . Since fs * ft = fs + t * f we have h ( f ̧ ) h ( ft ) = h ( fs + t ) h ( f ) , which shows ...
Page 2448
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping q : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
... continuous spectrum . In the present section we shall illustrate this assertion by proving a number of results , due ... continuous linear mapping q : A → B ( X ) , of norm at most M1 , is given ; ( b ) a continuous linear mapping ŋ : A ...
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