We establish maximality of the sum of two maximal monotone operators in general Banach space, assuming only the Rockafellar qualification assumption.

This contribution is concerned with a detailed investigation of linearity axioms for fuzzy orderings. Different existing concepts are evaluated with respect to three fundamental correspondences from the classical case—linearizability of partial orderings, intersection representation, and one-to-one correspondence between linearity and maximality. As a main result, we obtain that it is virtually...

As our proof depends only on the invariant subspace theorem for H1 [2, Theorem 7 ] ; see also [4 ], where Hl denotes the L1 closure of A, and the F. and M. Riesz theorem [3, p. 47], it works in any situation in which these two theorems are valid. Some algebras in which both theorems are valid were considered by Bishop [l]. Even though the proof extracted by Cohen [3, p. 94] from the proof of We...

We point out the geometric significance of a part of the theorem regarding the maximality of the orthogonal group in the equiaffine group proved in [12].

Working constructively, we discuss two types of maximality for ideals in a commutative ring with identity, showing also that the results are the best possible.

Using some advanced properties of the de Groot dual and some generalization of the Hofmann-Mislove theorem, we solve in the positive the question of D. E. Cameron: Is every compact topology contained in some maximal compact topology? Date: 29. 8. 2004. Last revision: 14. 10. 2004