Generalized dissipativeness in a Banach space

David R. Gurney

International Journal of Mathematics and Mathematical Sciences, 1996, vol. 19, 1-8

Abstract:

Suppose X is a real or complex Banach space with dual X * and a semiscalar product [ , ] . For k a real number, a subset B of X × X will be called k - dissipative if for each pair of elements ( x 1 , y 1 ) , ( x 2 , y 2 ) in B , there exists h ∈ { f ∈ X * : [ x , f ] = | x | 2 = | f | 2 } such that Re [ y 1 − y 2 , h ] ≤ k | x 1 − x 2 | 2 . This definition extends a notion of dissipativeness which is equivalent to having k equal zero here. A number of definitions and theorems related to this original dissipative notion are generalized in the present paper to fit the k -dissipative situation, and proofs are given for the new theorems.

Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:926173

DOI: 10.1155/S0161171296000051

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