Mathematics – Functional Analysis
Scientific paper
2009-09-14
Mathematics
Functional Analysis
Scientific paper
In this paper, we give two explicit examples of unbounded linear maximal monotone operators. The first unbounded linear maximal monotone operator $S$ on $\ell^{2}$ is skew. We show its domain is a proper subset of the domain of its adjoint $S^*$, and $-S^*$ is not maximal monotone. This gives a negative answer to a recent question posed by Svaiter. The second unbounded linear maximal monotone operator is the inverse Volterra operator $T$ on $L^{2}[0,1]$. We compare the domain of $T$ with the domain of its adjoint $T^*$ and show that the skew part of $T$ admits two distinct linear maximal monotone skew extensions. These unbounded linear maximal monotone operators show that the constraint qualification for the maximality of the sum of maximal monotone operators can not be significantly weakened, and they are simpler than the example given by Phelps-Simons. Interesting consequences on Fitzpatrick functions for sums of two maximal monotone operators are also given.
Bauschke Heinz H.
Wang Xianfu
Yao Liangjin
No associations
LandOfFree
Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Examples of discontinuous maximal monotone linear operators and the solution to a recent problem posed by B.F. Svaiter will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-554916