Linear Operators: Spectral operators |
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Page 2239
... follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover , statement ( g ) follows from Corollary 7 . Statement ( d ) is obvious . Letting e € 2。 and x = E ( e ) X , we have = Tfxe ) x lim T ( ƒxe ) E ( en ) ...
... follows from Lemma 6 that T ( f ) is a closed , densely defined operator . Moreover , statement ( g ) follows from Corollary 7 . Statement ( d ) is obvious . Letting e € 2。 and x = E ( e ) X , we have = Tfxe ) x lim T ( ƒxe ) E ( en ) ...
Page 2246
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin C ) ... follows that ( sin #C ) ” P ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
... follows from Corollary 4 and Theorem 9 ( i ) that F com- mutes with E. By Theorem 9 ( ii ) , the restriction ( sin C ) ... follows that ( sin #C ) ” P ( n ) H = { 0 } . Let e be a closed set in the complex plane not containing zero . Then ...
Page 2459
... follows at once . If xn € Σac ( H ) and lim∞ = x , then , by what we have already proved , we may write x = y1 + y2 + ys , where y1 E Zac ( H ) and yY2 , Yз are orthogonal to Σac ( H ) . But , since x , € Σac ( H ) we have ( în , y ) ...
... follows at once . If xn € Σac ( H ) and lim∞ = x , then , by what we have already proved , we may write x = y1 + y2 + ys , where y1 E Zac ( H ) and yY2 , Yз are orthogonal to Σac ( H ) . But , since x , € Σac ( H ) we have ( în , y ) ...
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