Some characterizations of frames in ℓ²(I; H) and topological applications

• El Idrissi, Nizar ^[1] ; Kabbaj, Samir ^[1] ; Moalige, Brahim
  1. [1] Université Ibn Tofail.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 5, 2022, págs. 1141-1152
• Idioma: inglés
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• Resumen

  • We propose in this article some characterizations of the notion of frame in ℓ²(I; H). The first one is general, and depends on a procedure of inserting a family of vectors instead of x in the definition of a frame. This allows us to define the analysis, synthesis and frame operator on the space ℓ²(I; H) instead of H. The second one is specific to ℓ² (I; Ck) and relate it to the freeness of the finite set of components of the frame. The third one concerns normalised tight frames in ℓ²(I; Ck). Afterwards, we give an example of a frame in ℓ²(I; C²) using another sufficient condition in dimension 2. We conclude with some topological applications of these characterizations.