2018/02/18 by Gh. Abbaspour Tabadkan, Tabadkan, GH. Abbaspour, Hossein-nezhad, H. +2
Mathematics · #47A05 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Primary 42C15 #Secondary 46C05 #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1802.06363
openalex publication_date 2018/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notation of generalized Bessel multipliers is obtained by a bounded operator on ℓ2 which is inserted between the analysis and synthesis operators. We show that various properties of generalized multipliers are closely related to their parameters, in particular it will be shown that the membership of generalized Bessel multiplier in the certain operator classes requires that its symbol belongs in the same classes, in special sense. Also, we give some examples to illustrate our results. As we shall see, generalized multipliers associated with Riesz bases are well-behaved, more precisely in this case multipliers can be easily composed and inverted. Special attention is devoted to the study of invertible generalized multipliers. Sufficient and/or necessary conditions for invertibility are determined. Finally, the behavior of these operators under perturbations is discussed.