{"title":"Exact sequences for dual Toeplitz algebras on hypertori","authors":"Lakhdar Benaissa, Hocine Guediri","doi":"10.1007/s40065-022-00408-7","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk <span>\\({\\mathbb {D}}^n\\)</span> in the unitary space <span>\\({\\mathbb {C}}^n\\)</span>, that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus <span>\\({\\mathbb {T}}^n\\)</span>.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"12 1","pages":"71 - 81"},"PeriodicalIF":0.9000,"publicationDate":"2022-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-022-00408-7.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-022-00408-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk \({\mathbb {D}}^n\) in the unitary space \({\mathbb {C}}^n\), that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus \({\mathbb {T}}^n\).
在本文中，我们构造了一个符号演算，产生对偶Toeplitz代数的短精确序列，该代数由与幺正空间中的多盘（｛\mathbb｛C｝｝^n\）相关的Hardy空间上的所有有界对偶Toepliz算子生成，在我们的早期论文（Benaissa and Guediri In台湾J Math 19:31–492015）中已经引入并进行了充分研究，以及由对偶Toeplitz算子生成的C*-子代数，该算子具有在相关超轨道上连续的符号。
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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