Narrow Results

In this paper, we introduce controlled frames in Hilbert $C^{\ast }$-modules and we show that they share many useful properties with their corresponding notions in Hilbert space. Next, we give a characterization of controlled frames in Hilbert $C^{\ast }$-module. Also multiplier operators for controlled frames in Hilbert $C^{\ast }$-modules will be defined and some of its properties will be shown. Finally, we investigate weighted frames in Hilbert $C^{\ast }$-modules and verify their relations to controlled frames and multiplier operators.

The main purpose of this paper is to introduce the notion of *-T-controlled frames in Hilbert $C^{*}$-modules. We present some results of frames in the view of *-T-controlled frames in Hilbert $C^{*}$-modules. Also, we define *-w-frames and give their relations to *-T-controlled frames and multiplier operators.

The author establishes a deLeeuw-type theorem on maximal multiplier operators on local Hardy-Lorentz space.

In this paper, associated with convolutions, linear operators ${𝒟}([\alpha ])$ and ${ℐ}([\alpha ])$ are defined with the requirement of certain recurring relations. Some results based on analytic functions involving these operators are derived. Taking some specific forms of such operators, results involving the Dziok–Srivastava operator, the Jung–Kim–Srivastava integral operator, the Srivastava–Attiya linear operator and others, are also mentioned.