Linear Operators: Spectral operators |
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Page 2029
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фп Ф T , ( p ) = { __p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
... determined by a bounded finitely additive set function v ( defined on some field of sets in RN which includes the open sets ) by the equation ( 48 ) Фп Ф T , ( p ) = { __p ( s ) v ( ds ) , RN ΚΕΦ . Similarly , functions on RN may determine ...
Page 2184
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let 2 be an algebra of operators in the complex B - space X which is the ...
... determined spectral measure . This is the analogue of the general spectral theorem for algebras of normal operators in Hilbert space ( cf. X.2.1 ) . 4 THEOREM . Let 2 be an algebra of operators in the complex B - space X which is the ...
Page 2316
... determined so as to satisfy ko 18h 1 sin Bn = cos ßn . It follows readily that so that It follows that Вп πT = 2 - ( nako ) -1 + 0 ( n - 2 ) , Pn ( t ) = cos ( snt + Sn ) , Sn = ( nπko ) 1 + O ( n − 2 ) . 1 S " ( Pn ( 1 ) ) 2 dt ~ ၂၀ ...
... determined so as to satisfy ko 18h 1 sin Bn = cos ßn . It follows readily that so that It follows that Вп πT = 2 - ( nako ) -1 + 0 ( n - 2 ) , Pn ( t ) = cos ( snt + Sn ) , Sn = ( nπko ) 1 + O ( n − 2 ) . 1 S " ( Pn ( 1 ) ) 2 dt ~ ၂၀ ...
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