Some relations between dualities, polarities, coupling functionals, and conjugations. (English) Zbl 0601.46043

Some relations concerning generalizations of duality, polarity and conjugate functionals are proved. The author uses concepts of Evers, Maaren and others from the 80’s.
A typical result from the paper: there is a natural equivalence between polarities and dualities (Theorem 1.1). Here duality is a mapping \(2^ X\to 2^ W\) with De Morgan identity. Many of the cited papers under printing being preparations, the paper contains these definitions, consequently, it is well-readable. Numerous examples and remarks help to show the critical assumptions of the corresponding concepts.
Reviewer: A.P.Bosznay


46E99 Linear function spaces and their duals
46B10 Duality and reflexivity in normed linear and Banach spaces
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