Linear Operators: Spectral operators |
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Page 2172
... Let Xl and let T be defined for x = = ∞ l to be the element y = ( 1 , 2 , ... ) , where ∞ 71-1- ( 1-1 ) . 1 ; Nn ... F be defined for each Borel set σ by F ( o ) = E ( o ) + AE ( 0 ) — E ( o ) A . Show that F is a bounded spectral ...
... Let Xl and let T be defined for x = = ∞ l to be the element y = ( 1 , 2 , ... ) , where ∞ 71-1- ( 1-1 ) . 1 ; Nn ... F be defined for each Borel set σ by F ( o ) = E ( o ) + AE ( 0 ) — E ( o ) A . Show that F is a bounded spectral ...
Page 2190
Nelson Dunford, Jacob T. Schwartz. Then the map f → S ( f ) is an isomorphism between the B - algebra EB ( A , Σ ) ... let f = = 1 Xo , where the sets o1 , ... , σ , are dis- Σ α joint sets in whose union is A. There is an i 。≤n with E ...
Nelson Dunford, Jacob T. Schwartz. Then the map f → S ( f ) is an isomorphism between the B - algebra EB ( A , Σ ) ... let f = = 1 Xo , where the sets o1 , ... , σ , are dis- Σ α joint sets in whose union is A. There is an i 。≤n with E ...
Page 2248
... Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p ... f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a spectral operator ...
... Let f be a function analytic in a domain U which , when taken together with a finite number of exceptional points p ... f has at most a pole at each of the excep- tional points p and at infinity . Then f ( T ) is a spectral operator ...
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