Integral operator frames on Hilbert C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{*}$$\end{document}-modules

被引:0
作者
Nadia Assila [1 ]
Hatim Labrigui [1 ]
Abdeslam Touri [1 ]
Mohamed Rossafi [2 ]
机构
[1] Ibn Tofail University,Department of Mathematics, Faculty of Sciences
[2] University Sidi Mohamed Ben Abdellah,Department of Mathematics, Faculty of Sciences Dhar El Mahraz
关键词
Frames; Operator frame; -algebras; Hilbert ; -modules; Primary 42C15; Secondary 46L05;
D O I
10.1007/s11565-024-00501-z
中图分类号
学科分类号
摘要
Introduced by Duffin and Schaefer as a part of their work on nonhamonic Fourier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field. In this work, we introduce a new concept that of integral operator frame for the set of all adjointable operators on a Hilbert C∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^{*}$$\end{document}-modules H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {H}}$$\end{document} and we give some new properties relating for some construction of integral operator frame, also we establish some new results. Some illustrative examples are provided to advocate the usability of our results.
引用
收藏
页码:1271 / 1284
页数:13
相关论文
共 36 条
  • [1] Alijani A(2011)-frames in Hilbert U.P.B. Sci. Bull. Ser. A 73 89-106
  • [2] Dehghan MA(2007)-modules Proc. Am. Math. Soc. 135 469-478
  • [3] Arambašić L(2021)On frames for countably generated Hilbert Moroccan J. Pure Appl. Anal 7 116-133
  • [4] Assila N(1952)-modules Trans. Am. Math. Soc. 72 341-366
  • [5] Kabbaj S(2002)Controlled J. Oper. Theory 48 273-314
  • [6] Moalige B(2012)-Fusion frame for Hilbert spaces Appl. Comput. Harmon. Anal. 32 139-144
  • [7] Duffin RJ(2020)A class of nonharmonic fourier series Moroccan J. Pure Appl. Anal. (MJPAA) 6 184-197
  • [8] Schaeffer AC(2018)Frames in Hilbert Wavelets and Linear Algebra 5 1-13
  • [9] Frank M(1953)-modules and Am. J. Math. 75 839-858
  • [10] Larson DR(2007)-algebras Proc. Indian Acad. Sci. Math. Sci. 117 1-12