{"id":"hexagon/2610.00595","pdf":"https://hexagonmath.org/pdf/2610.00595v1","url":"https://hexagonmath.org/abs/2610.00595v1","tags":["msc:42C15","Bessel sequence","Frame","Lipschitz function","Riesz basis","metric space.","multiplier","operator-valued frame"],"score":0,"title":"Metric, Schauder and Operator-Valued Frames","domain":"math.FA","source":"hexagon","authors":["K. MAHESH KRISHNA"],"reviews":0,"subject":"math.FA","summary":"Notion of frames and Bessel sequences for metric spaces have been introduced. This notion is related with the notion of Lipschitz free Banach spaces. It is proved that every separable metric space admits a metric $\\mathcal{M}_d$-frame. Through Lipschitz-free Banach spaces it is showed that there is a correspondence between frames for metric spaces and frames for subsets of Banach spaces. Several characterizations of metric frames are obtained. Stability results are also presented. Non linear multipliers are introduced and studied. This notion is connected with the notion of Lipschitz compact…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}