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BIBTEX RIS

Existence of a spectrum for nonlinear transformations

1969; Mathematical Sciences Publishers; Volume: 31; Issue: 1 Linguagem: Inglês

10.2140/pjm.1969.31.157

ISSN

1945-5844

Autores

John M. Neuberger,

Tópico(s)

Stability and Controllability of Differential Equations

Resumo

Denote by S a complex (nondegenerate) Banach space.Suppose that T is a transformation from a subset of S to S. A complex number λ is said to be in the resolvent of T if (21 -T)"1 exists, has domain £ and is Frέchet differentiate (i.e., if p is in S there is a unique continuous linear transformation F= [(21-T)-1 ]^) from S to £ so that T)^q-(2I-T)^p -F(qp) || = 0)and locally Lipschitzean everywhere on S. A complex number is said to be in the spectrum of T if it is not in the resolvent of T. Suppose in addition that the domain of T contains an open subset of S on which T is Lipschitzean.THEOREM.T has a (nonempty) spectrum.

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