Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras
In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of mult...
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| Format: | Article |
| Language: | English |
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University of Maragheh
2019-10-01
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| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf |
| _version_ | 1818144102441549824 |
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| author | Mona Naroei Irani Akbar Nazari |
| author_facet | Mona Naroei Irani Akbar Nazari |
| author_sort | Mona Naroei Irani |
| collection | DOAJ |
| description | In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ { {h_i} }_{i in I} }$ is a standard $ ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ ast $-frames in Hilbert modules over pro-C*-algebras are studied. |
| first_indexed | 2024-12-11T11:42:13Z |
| format | Article |
| id | doaj.art-300db73be33546ed9ff1ce53a8baf93d |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-11T11:42:13Z |
| publishDate | 2019-10-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-300db73be33546ed9ff1ce53a8baf93d2022-12-22T01:08:35ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-10-0116110511710.22130/scma.2018.75253.32836278Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebrasMona Naroei Irani0Akbar Nazari1Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran.Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modules over pro-C*-algebras and investigate conditions that under which the sequence ${ { {h_i} }_{i in I} }$ is a standard $ ast $-frame of multipliers for Hilbert modules over pro-C*-algebras. Also the effect of operators on standard $ ast $-frames of multipliers for $ E $ is examined. Finally, compositions of standard $ ast $-frames in Hilbert modules over pro-C*-algebras are studied.http://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdfHilbert modules over pro-C*-algebrasStandard $ ast $-frame of multipliers$ ast $-frame operatorPre-$ ast $-frame |
| spellingShingle | Mona Naroei Irani Akbar Nazari Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras Sahand Communications in Mathematical Analysis Hilbert modules over pro-C*-algebras Standard $ ast $-frame of multipliers $ ast $-frame operator Pre-$ ast $-frame |
| title | Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras |
| title_full | Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras |
| title_fullStr | Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras |
| title_full_unstemmed | Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras |
| title_short | Some Properties of $ ast $-frames in Hilbert Modules Over Pro-C*-algebras |
| title_sort | some properties of ast frames in hilbert modules over pro c algebras |
| topic | Hilbert modules over pro-C*-algebras Standard $ ast $-frame of multipliers $ ast $-frame operator Pre-$ ast $-frame |
| url | http://scma.maragheh.ac.ir/article_36278_bf43f599dbf871d99cf80e3655101b74.pdf |
| work_keys_str_mv | AT monanaroeiirani somepropertiesofastframesinhilbertmodulesoverprocalgebras AT akbarnazari somepropertiesofastframesinhilbertmodulesoverprocalgebras |