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M-dissipative-operator

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Let be a real Banach space with dual space X ^ { * } and normalized duality mapping J (cf. also Duality; Adjoint space). An operator T : X \supset D ( T ) \rightarrow 2 ^ { X } is called dissipative if for every x , y \in D ( T ) and every u \in T x , v \in T y there exists a j \in J ( x - y ) such that \langle u - v , j \rangle \leq 0 (cf. also Dissipative operator). A dissipative operator T is called m-dissipative if \lambda I - T is surjective for all \lambda > 0. Thus, an operator T is dissipative (respectively, m-dissipative) if and only if the operator - T is accretive (respectively, m-accretive). For more information, see Accretive mapping and m-accretive operator.

How to Cite This Entry:
M-dissipative-operator. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=M-dissipative-operator&oldid=50267
This article was adapted from an original article by A.G. Kartsatos (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article