Gelfand-Philips and L-limited properties of order P on Banach spaces

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  • M. Alikhani Department of Mathematics ,University of Isfahan, Isfahan, Iran
  • M. Fakhar Department of Mathematics ,University of Isfahan, Isfahan, Iran
  • Jafar Zafarani Sheukhbahaee University

Abstract

In this paper we show the stability of Gelfand-Phillips property of order $p$ under taking injective tensor product, compact operators, and Bochner integrable functions. We introduce the concept of $ L $-limited sets of order $p,$ and obtain some characterizations of limited $p$-convergent operators. Also we define the notion of $L$-limited of order $p$ and characterize this property in terms of weak compact operators.\ Furthermore, we give a new dual characterization of the class of weak$^{\ast}$ $p$-convergent operators through $ L $-limited sets of order $ p. $\ Moreover, some characterizations of the Gelfand-Phillips property of order $p$ in terms of limited $ p $-convergent operators are given.\ In addition by applying our results on the limited $ p $-convergent operators, we obtain some characterizations of the Dunford-Pettis$ ^{\ast} $ property of order $p.$

Published
Aug 27, 2018
How to Cite
ALIKHANI, M.; FAKHAR, M.; ZAFARANI, Jafar. Gelfand-Philips and L-limited properties of order P on Banach spaces. Nonlinear Studies, [S.l.], v. 25, n. 3, p. 689-700, aug. 2018. ISSN 2153-4373. Available at: <http://nonlinearstudies.com/index.php/nonlinear/article/view/1552>. Date accessed: 22 sep. 2018.