Linear Operators: Spectral operators |
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Page 1951
... linear subspace of X , then the set of bounded linear operators A in X for which AX is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ( o ) ...
... linear subspace of X , then the set of bounded linear operators A in X for which AX is a closed right ideal in B ( X ) . Thus the following statement is an immediate corollary of Theorem 2 . 5 COROLLARY . The ranges of S , N , and E ( o ) ...
Page 1960
... linear map A : x → y of HP into itself , it is easy to define a set a ,, of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in Ho and let H , be ...
... linear map A : x → y of HP into itself , it is easy to define a set a ,, of p2 bounded linear maps in 5 such that the equation y = Ax is equivalent to the system ( 4 ) . To see this , let A be a bounded linear map in Ho and let H , be ...
Page 2400
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
... linear operator in X ; let K be a second linear operator in X which is , in a sense to be made precise below , very small relative to T. Following Friedrichs , we may then surmise that T + K and T are similar operators , that is , that ...
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