Linear Operators: Spectral operators |
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Results 1-3 of 89
Page 1953
... range of V is closed . Let y be in the closure of the range of V. Then for some sequence { x } in E ( { 0 } ' ) X_we have Vxy and , since the range of T is closed , there is an x in X with Tx y . Hence VE ( { 0 } ' ) x = TE ( { 0 } ...
... range of V is closed . Let y be in the closure of the range of V. Then for some sequence { x } in E ( { 0 } ' ) X_we have Vxy and , since the range of T is closed , there is an x in X with Tx y . Hence VE ( { 0 } ' ) x = TE ( { 0 } ...
Page 1954
... range if and only if = 0 is either in the resolvent set of T or an isolated ( i ) the point spectral point of T , and ( ii ) the operator TE ( { 0 } ) has a closed range . PROOF . Let T have a closed range . We have already proved ( i ) ...
... range if and only if = 0 is either in the resolvent set of T or an isolated ( i ) the point spectral point of T , and ( ii ) the operator TE ( { 0 } ) has a closed range . PROOF . Let T have a closed range . We have already proved ( i ) ...
Page 2312
... range of T , and hence for all y in the closure of the range of T. On the other hand , if y is not in the closure of the range of T , then by the Hahn - Banach theorem ( II.3.13 ) there exists a y * in Y * such that y * ( y ) # 0 , y ...
... range of T , and hence for all y in the closure of the range of T. On the other hand , if y is not in the closure of the range of T , then by the Hahn - Banach theorem ( II.3.13 ) there exists a y * in Y * such that y * ( y ) # 0 , 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