Linear Operators: Spectral operators |
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Page 2312
... space X. Let f * , f * , f * be a basis for the solutions of the equation ( T * −λ 。) ƒ * = 0 and let Σ be the ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
... space X. Let f * , f * , f * be a basis for the solutions of the equation ( T * −λ 。) ƒ * = 0 and let Σ be the ... Banach space . It is well to remark , how- ever , that in the special case in which the Banach space is Hilbert space ...
Page 2313
... Banach space adjoint , contrary to our practice in other Banach spaces . This has the effect of introducing complex conjugates in many of the Hilbert - space formulas where the corresponding Banach - space formulas do not have complex ...
... Banach space adjoint , contrary to our practice in other Banach spaces . This has the effect of introducing complex conjugates in many of the Hilbert - space formulas where the corresponding Banach - space formulas do not have complex ...
Page 2514
... spaces and decomposable operators . Rev. Roumaine Math . Pures Appl . 12 , 607–610 ( 1967 ) . 16. Some properties of a couple of operators on a Banach space . Rev. Roumaine Math . Pures Appl . 12 , 1005–1010 ( 1967 ) . 17. On some ...
... spaces and decomposable operators . Rev. Roumaine Math . Pures Appl . 12 , 607–610 ( 1967 ) . 16. Some properties of a couple of operators on a Banach space . Rev. Roumaine Math . Pures Appl . 12 , 1005–1010 ( 1967 ) . 17. On some ...
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