Linear Operators: Spectral operators |
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Page 1947
... bounded Boolean algebras of projections in a Hilbert space . Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean ...
... bounded Boolean algebras of projections in a Hilbert space . Then there exists a bounded self adjoint operator B in H with a bounded everywhere defined inverse such that BEB - 1 is a self adjoint projection for every E in the Boolean ...
Page 2239
Nelson Dunford, Jacob T. Schwartz. Since fxe is a bounded function , the operator T ( f Xe ) is a bounded operator . Xe If x is in E ( e ) X as well as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf ...
Nelson Dunford, Jacob T. Schwartz. Since fxe is a bounded function , the operator T ( f Xe ) is a bounded operator . Xe If x is in E ( e ) X as well as in E ( e ) X , it follows from the operational calculus for bounded functions ( cf ...
Page 2361
... bounded domains covering the whole complex plane , and suppose that lim¿ → ∞ minze u¡ | z❘ = ∞ . Let V¡ be the boundary of U¡ . Let 0 ≤ v < 1 , and put Mi = max λενί , μεσ ( Τ ) - - V Let λo o ( T ) , and let P be an operator such ...
... bounded domains covering the whole complex plane , and suppose that lim¿ → ∞ minze u¡ | z❘ = ∞ . Let V¡ be the boundary of U¡ . Let 0 ≤ v < 1 , and put Mi = max λενί , μεσ ( Τ ) - - V Let λo o ( T ) , and let P be an operator such ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero