Uniqueness of the algebraic multiplicity
Given a smooth function £ of a real or complex variable and taking its values in the class of Fredholm operators of index zero in a Banach space, there are some available definitions in the literature of algebraic multiplicity of the family £ at a point x0 of the parameter at which the operator £(x0...
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| Format: | Journal article |
| Language: | English |
| Published: |
2004
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| Summary: | Given a smooth function £ of a real or complex variable and taking its values in the class of Fredholm operators of index zero in a Banach space, there are some available definitions in the literature of algebraic multiplicity of the family £ at a point x0 of the parameter at which the operator £(x0) becomes non-invertible. The purpose of this paper is to suggest an axiomatic for the multiplicity and to prove that the algebraic multiplicity is uniquely determined by a few of its properties, independently of its construction. |
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