SOME TOPOLOGICAL STRUCTURES OF NORMED SPACE VALUED ORLICZ FUNCTION SPACE ( l∞ (U, V, || . ||, Ω )) - Pokhrel, Jagat (Journal of Global Research in Mathematical Archives(JGRMA), 2018)
The aim of this work is to study new classes l∞ (U, V, || . ||, Ω ) and l∞(U, V, || . ||, Ω, λ) of normed space valued function space using Orlicz function Ω as the generalizations of well known complex basic sequence space l∞ studied in Functional Analysis. These results can be used for further generalization to investigate the various properties of existing Orlicz function spaces. Besides the investigation of linear topological structures of the class l∞ (U, V, || . ||, Ω ) <!--[if gte mso 9]> Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 <![endif]--><!--[if gte mso 9]> <![endif]--><!--[if gte mso 10]> <![endif]--><span style="font-size: 10.0pt; font-family: 'Times','serif'; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">when topologized it with suitable natural norm, our primarily interest is to explore the various conditions pertaining to the inclusion of the class l∞(U, V, || . ||, Ω, λ) <!--[if gte mso 9]> Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 <![endif]--><!--[if gte mso 9]> <![endif]--><!--[if gte mso 10]> <![endif]--><span style="font-size: 10.0pt; font-family: 'Times','serif'; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">in terms of different values of λ.<!--[if gte mso 9]> Normal 0 false false false EN-US X-NONE X-NONE MicrosoftInternetExplorer4 <![endif]--><!--[if gte mso 9]> <![endif]--><!--[if gte mso 10]> <![endif]--><span style="font-size: 10.0pt; font-family: 'Times','serif'; mso-fareast-font-family: 'Times New Roman'; color: black; mso-themecolor: text1; mso-ansi-language: EN-US; mso-fareast-language: EN-US; mso-bidi-language: AR-SA;">when topologized it with suitable natural norm, our primarily interest is to explore the various conditions pertaining to the inclusion of the class