# M-dissipative-operator

From Encyclopedia of Mathematics

Let be a real Banach space with dual space and normalized duality mapping (cf. also Duality; Adjoint space). An operator is called dissipative if for every and every there exists a such that (cf. also Dissipative operator). A dissipative operator is called -dissipative if is surjective for all . Thus, an operator is dissipative (respectively, -dissipative) if and only if the operator is accretive (respectively, -accretive). For more information, see Accretive mapping and -accretive operator.

**How to Cite This Entry:**

M-dissipative-operator. A.G. Kartsatos (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=M-dissipative-operator&oldid=11944

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098