On the range of the sum of monotone operators in general Banach spaces

Riahi, Hassan

doi:10.1090/S0002-9939-96-03314-X

On the range of the sum of monotone operators in general Banach spaces
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by Hassan Riahi

Proc. Amer. Math. Soc. 124 (1996), 3333-3338

DOI: https://doi.org/10.1090/S0002-9939-96-03314-X

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Abstract:

The purpose of this paper is to generalize the Brézis-Haraux theorem on the range of the sum of monotone operators from a Hilbert space to general Banach spaces. The result obtained provides that the range $\mathcal R(\overline {A+B}{}^\tau )$ is topologically almost equal to the sum $\mathcal R(A)+\mathcal R(B)$ where $\tau$ is a compatible topology in $X^{**}\times X^*$ as proposed by Gossez. To illustrate the main result we consider some basic properties of densely maximal monotone operators.

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