A throrcm concerning the completeness of operator manifolds used for the generation of ionized electronic states by direct methods is formulated and proven.
A moment theorem for completely hyperexpansive operators
✍ Scribed by Z. J. Jabłoński
- Publisher
- Akadmiai Kiad
- Year
- 2007
- Tongue
- English
- Weight
- 362 KB
- Volume
- 120
- Category
- Article
- ISSN
- 1588-2632
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📜 SIMILAR VOLUMES
## Abstract Some expansion and completeness theorems for operator manifolds, which are currently being employed in propagator theory, are derived. It is shown that excitation or ionization operators satisfying the conditions __Q__|0〉 = |Λ〉 and __Q__~Λ~|0〉 = 0 for general excited states |Λ〉 and refe
A bounded linear operator T on a complex Hilbert space will be called completely indecomposable if its spectrum is not a singleton, and is included in the spectrum of the restrictions of T and T \* to any of their nonzero invariant subspaces. Two classes of completely indecomposable operators are co
The purpose of this note is to show that the answers to Problems 2, 3, and 5 in [1] are positive, even under weaker assumptions. Keeping the notations of [1], we have Theorem 1. If : is a positive sequence on Z + which converges to a nonzero limit, then the operator A(:) has a proper invariant subsp