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We introduce smooth p -order ideals (1≤p≤∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$1\le p\le \infty$$\end{document}) to initiate the studies of ideals in non-unital ordered normed spaces. We obtain some order-theoretic properties and examples of these ideals. Furthermore, we show that every semi-M-ideal in affine space A(K) is smooth ∞\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\infty$$\end{document}-order ideal. Moreover, we derive that every smooth 1-order ideal is an L-summand in order smooth 1-normed space.
Advances in Operator Theory – Springer Journals
Published: Apr 19, 2021
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