- Iğdır Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Cilt: 15 Sayı: 1
- Vector Valued Multipliers of Invariant Means and Compact Summing Operators
Vector Valued Multipliers of Invariant Means and Compact Summing Operators
Authors : Mahmut Karakuş
Pages : 298-307
Doi:10.21597/jist.1534364
View : 50 | Download : 42
Publication Date : 2025-03-01
Article Type : Research Paper
Abstract :In notation of multiplier convergence, one can redefine the notion generalized Köthe-Toeplitz dual of a sequence space. Since the basis (e^n) of a sequence space N dominates the sequence (v_n)∈N^β, the β-(generalized Köthe-Toeplitz) dual of N can be represented as N^β={(v_n)|(e^n)> ̃(v_n)}. Employing usual terminology and concepts, in this paper, we introduce novel vector-valued multiplier spaces through the σ-summability method alongside a sequence of bounded linear operators. These spaces are equipped with the sup norm topology. Building on the foundational comprehension of completeness of normed spaces, we examine some properties of the summing operator S in detail, which acts between multiplier spaces and general normed spaces. This investigation entails a meticulous characterization of the operator\\\'s various properties. By examining these properties through the frameworks of some types of multiplier series, we deliver a thorough and refined analysis of the operator’s behavior, providing a more expansive and enriched perspective on its functional characteristics.Keywords : σ -yakınsaklık, Sınırlı çarpan yakınsak seriler, c_0 (X)-çarpan yakınsak seriler, Toplam operatörler, Toplanabilme
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