International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 25-32
Generalized dissipativeness in a Banach space
Southeastern Louisiana University, SLU 541, Hammond 70402, LA, USA
Received 12 December 1994
Copyright © 1996 David R. Gurney. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Suppose is a real or complex Banach space with dual and a semiscalar product . For a real number, a subset of will be called -dissipative if for each pair of elements , in , there existssuch thatThis definition extends a notion of dissipativeness which is equivalent to having equal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit the -dissipative situation, and proofs are given for the new theorems.