A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}
Complex Anal. Oper. Theory 18, 75 (2024) Using the Wold-von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over $\mathbb{N}_0^{k}....
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| creator | Saini, Dimple Trivedi, Harsh Veerabathiran, Shankar |
| description | Complex Anal. Oper. Theory 18, 75 (2024) Using the Wold-von Neumann decomposition for the isometric covariant
representations due to Muhly and Solel, we prove an explicit representation of
the commutant of a doubly commuting pure isometric representation of the
product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete
characterization of invariant subspaces for a doubly commuting pure isometric
representation of the product system. This provides us a complete set of
isomorphic invariants. Finally, we classify a large class of commuting
isometric representations of the product system. |
| doi_str_mv | 10.48550/arxiv.2308.16674 |
| format | Article |
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representations due to Muhly and Solel, we prove an explicit representation of
the commutant of a doubly commuting pure isometric representation of the
product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete
characterization of invariant subspaces for a doubly commuting pure isometric
representation of the product system. This provides us a complete set of
isomorphic invariants. Finally, we classify a large class of commuting
isometric representations of the product system.</description><identifier>DOI: 10.48550/arxiv.2308.16674</identifier><language>eng</language><subject>Mathematics - Operator Algebras</subject><creationdate>2023-08</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2308.16674$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2308.16674$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1007/s11785-024-01520-6$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Saini, Dimple</creatorcontrib><creatorcontrib>Trivedi, Harsh</creatorcontrib><creatorcontrib>Veerabathiran, Shankar</creatorcontrib><title>A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}</title><description>Complex Anal. Oper. Theory 18, 75 (2024) Using the Wold-von Neumann decomposition for the isometric covariant
representations due to Muhly and Solel, we prove an explicit representation of
the commutant of a doubly commuting pure isometric representation of the
product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete
characterization of invariant subspaces for a doubly commuting pure isometric
representation of the product system. This provides us a complete set of
isomorphic invariants. Finally, we classify a large class of commuting
isometric representations of the product system.</description><subject>Mathematics - Operator Algebras</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotjz1PwzAURb0woMIPYMIDa4JTO048VhVfUgVLR0T07NiqBYmjZzeiVP3vpIHpvuGep3sIuSlYLuqyZPeA337Ml5zVeSFlJS7JsKJmBwgmWfQ_kHzoaXDU9yOghz7RuNdxAGMjdQGpj6GzCb2haAe00fZpZuIZGjC0ezMhh5hsR8Nokd69d5B2Wh9fTw37OH6ersiFg69or_9zQbaPD9v1c7Z5e3pZrzYZTLsy12ol21ZxqEAwp0DUoHkhFF9yJTVoURaVcVXFTWGnc-pAq2Q91ZhmQvAFuf17Oys3A_oO8NCc1ZtZnf8CMZZW4g</recordid><startdate>20230831</startdate><enddate>20230831</enddate><creator>Saini, Dimple</creator><creator>Trivedi, Harsh</creator><creator>Veerabathiran, Shankar</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20230831</creationdate><title>A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}</title><author>Saini, Dimple ; Trivedi, Harsh ; Veerabathiran, Shankar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a674-fdb96dd93a7a40f9a48ab314932396bab4517cf773c1e51740fad96848a0b0443</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics - Operator Algebras</topic><toplevel>online_resources</toplevel><creatorcontrib>Saini, Dimple</creatorcontrib><creatorcontrib>Trivedi, Harsh</creatorcontrib><creatorcontrib>Veerabathiran, Shankar</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Saini, Dimple</au><au>Trivedi, Harsh</au><au>Veerabathiran, Shankar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k}</atitle><date>2023-08-31</date><risdate>2023</risdate><abstract>Complex Anal. Oper. Theory 18, 75 (2024) Using the Wold-von Neumann decomposition for the isometric covariant
representations due to Muhly and Solel, we prove an explicit representation of
the commutant of a doubly commuting pure isometric representation of the
product system over $\mathbb{N}_0^{k}.$ As an application, we study a complete
characterization of invariant subspaces for a doubly commuting pure isometric
representation of the product system. This provides us a complete set of
isomorphic invariants. Finally, we classify a large class of commuting
isometric representations of the product system.</abstract><doi>10.48550/arxiv.2308.16674</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Operator Algebras |
| title | A characterization of invariant subspaces for isometric representations of product system over $\mathbb{N}_0^{k} |
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