{"title":"Banach空间$l_｛p｝\\left（\\mathbb｛BC｝\\lift（N\\right）\\right）$与$\\ast-$norm$\\overset｛..｝｛\\parallel｝。\\overset｛..｝｛\\parallel｝_｛2，l_｛p｝\\left（\\mathbb｛BC｝\\lift（N\\right）\\right）｝$和一些性质","authors":"Nilay Sager, B. Sağır","doi":"10.32513/tmj/19322008123","DOIUrl":null,"url":null,"abstract":"In this work, we construct vector spaces $l_{p}\\left( \\mathbb{BC}\\left(N\\right) \\right) $ of absolutely $p-$ summable $\\ast -$bicomplex sequences with the $\\ast -$ norm $\\overset{..}{\\parallel }.\\overset{..}{\\parallel }_{2,l_{p}\\left( \\mathbb{BC}\\left( N\\right) \\right) }$ over the field $\\mathbb{C}\\left( N\\right).$ Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in $\\mathbb{BC}\\left( N\\right) $ with respect to $\\overset{..}{\\parallel }.\\overset{..}{\\parallel }_{2}.$","PeriodicalId":43977,"journal":{"name":"Tbilisi Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Banach spaces $l_{p}\\\\left( \\\\mathbb{BC}\\\\left( N\\\\right) \\\\right) $ with the $\\\\ast -$ norm $\\\\overset{..}{\\\\parallel }.\\\\overset{..}{\\\\parallel }_{2,l_{p}\\\\left( \\\\mathbb{BC}\\\\left( N\\\\right) \\\\right) }$ and some properties\",\"authors\":\"Nilay Sager, B. Sağır\",\"doi\":\"10.32513/tmj/19322008123\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this work, we construct vector spaces $l_{p}\\\\left( \\\\mathbb{BC}\\\\left(N\\\\right) \\\\right) $ of absolutely $p-$ summable $\\\\ast -$bicomplex sequences with the $\\\\ast -$ norm $\\\\overset{..}{\\\\parallel }.\\\\overset{..}{\\\\parallel }_{2,l_{p}\\\\left( \\\\mathbb{BC}\\\\left( N\\\\right) \\\\right) }$ over the field $\\\\mathbb{C}\\\\left( N\\\\right).$ Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in $\\\\mathbb{BC}\\\\left( N\\\\right) $ with respect to $\\\\overset{..}{\\\\parallel }.\\\\overset{..}{\\\\parallel }_{2}.$\",\"PeriodicalId\":43977,\"journal\":{\"name\":\"Tbilisi Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tbilisi Mathematical Journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32513/tmj/19322008123\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tbilisi Mathematical Journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32513/tmj/19322008123","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Banach spaces $l_{p}\left( \mathbb{BC}\left( N\right) \right) $ with the $\ast -$ norm $\overset{..}{\parallel }.\overset{..}{\parallel }_{2,l_{p}\left( \mathbb{BC}\left( N\right) \right) }$ and some properties
In this work, we construct vector spaces $l_{p}\left( \mathbb{BC}\left(N\right) \right) $ of absolutely $p-$ summable $\ast -$bicomplex sequences with the $\ast -$ norm $\overset{..}{\parallel }.\overset{..}{\parallel }_{2,l_{p}\left( \mathbb{BC}\left( N\right) \right) }$ over the field $\mathbb{C}\left( N\right).$ Also, we show that some inclusion relations hold and these vector spaces are Banach spaces by using Minkowski's inequality in $\mathbb{BC}\left( N\right) $ with respect to $\overset{..}{\parallel }.\overset{..}{\parallel }_{2}.$
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