Dergiler / Constructive mathematical analysis (Online) / 2021 / Cilt: 4 - Sayı: 1

Weak A-frames and weak A-semi-frames

Weak A-frames and weak A-semi-frames

JEAN PIERRE ANTOINE, GIORGIA BELLOMONTE, CAMILLO TRAPANI

Sayfa
104–118
DOI
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Abstract

After reviewing the interplay between frames and lower semi-frames, we introduce the notion of lowersemi-frame controlled by a densely defined operator A or, for short, a weak lower A-semi-frame and we study its properties. In particular, we compare it with that of lower atomic systems, introduced by one of us (GB). We discuss dualityproperties and we suggest several possible definitions for weak A-upper semi-frames. Concrete examples are presented.