2,537 research outputs found
The asymmetric sandwich theorem
We discuss the asymmetric sandwich theorem, a generalization of the
Hahn-Banach theorem. As applications, we derive various results on the
existence of linear functionals that include bivariate, trivariate and
quadrivariate generalizations of the Fenchel duality theorem. Most of the
results are about affine functions defined on convex subsets of vector spaces,
rather than linear functions defined on vector spaces. We consider both results
that use a simple boundedness hypothesis (as in Rockafellar's version of the
Fenchel duality theorem) and also results that use Baire's theorem (as in the
Robinson-Attouch-Brezis version of the Fenchel duality theorem). This paper
also contains some new results about metrizable topological vector spaces that
are not necessarily locally convex.Comment: 17 page
Involutions and Trivolutions in Algebras Related to Second Duals of Group Algebras
We define a trivolution on a complex algebra as a non-zero
conjugate-linear, anti-homomorphism on , which is a generalized
inverse of itself, that is, . We give several characterizations of
trivolutions and show with examples that they appear naturally on many Banach
algebras, particularly those arising from group algebras. We give several
results on the existence or non-existence of involutions on the dual of a
topologically introverted space. We investigate conditions under which the dual
of a topologically introverted space admits trivolutions
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