V -dualities and ⊥-dualities

Abstract

We introduce and study dualities △:[Rbar]^x → [Rbar]^w (i.e., mappings f ε [Rbar]^x → f ^△ ε [Rbar]^w such that for all {f_i }iε1 ∈ R^x and all index sets I), which satisfy the additional condition and their duals, which are characterized as those dualities △^*:R^x → R^w for which , where ⊥ and ⊺ are two new binary operations on [Rbar], which we introduce here. Furthermore, we give a characterization of those Δ which are also conjugations. Some applications are also mentioned.

Keywords:

• Dualities
• conjugations
• coupling functions

AMS 1980 Subject Classification:

• Primary: 06 A 15
• Secondary:06 A 23