2020/01/15 by Mahesh Krishna K., K., Mahesh Krishna, P. Sam Johnson +1
Mathematics · #22D10 #28B05 #46G10 #47A13 #47B65 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Operator Algebras (math.OA) #Primary 42C15 #Secondary 46E40 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2001.05128
openalex publication_date 2020/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Operator-valued frame (G-frame), as a generalization of frame is introduced by Kaftal, Larson, and Zhang in Trans. Amer. Math. Soc., 361(12):6349-6385, 2009 and by Sun in J. Math. Anal. Appl., 322(1):437-452, 2006. It has been further extended in the paper arXiv:1810.01629 [math.OA] 3 October 2018, so as to have a rich theory on operator-valued frames for Hilbert spaces as well as for Banach spaces. The continuous version has been studied in this paper when the indexing set is a measure space. We study duality, similarity, orthogonality and stability of this extension. Several characterizations are given including a notable characterization when the measure space is a locally compact group. Variation formula, dimension formula and trace formula are derived when the Hilbert space is finite dimensional.