Local Ergodic Theorems for C0-Semigroups
Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on the Banach space ${X}$ into itself and let $A$ be their infinitesimal generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$ does not have the single valued extension property, which implies that $A...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext bestellen |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | |
|---|---|
| container_issue | |
| container_start_page | |
| container_title | |
| container_volume | |
| creator | Tajmouati, Abdelaziz Barki, Fatih |
| description | Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on
the Banach space ${X}$ into itself and let $A$ be their infinitesimal
generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$
does not have the single valued extension property, which implies that $A$ must
have a nonempty interior of the point spectrum. Furthermore, we introduce the
local mean ergodic for $C_0$-semigroup $T(t)$ at a vector $x\in X$ and we
establish some conditions implying that $T(t)$ is a local mean ergodic at $x$. |
| doi_str_mv | 10.48550/arxiv.1912.10947 |
| format | Article |
| fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1912_10947</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1912_10947</sourcerecordid><originalsourceid>FETCH-LOGICAL-a677-afcbf31b86fe209cefe692b31fcd2e5f8b087ea6aa8640357f73c014b29534b83</originalsourceid><addsrcrecordid>eNotzrlqw0AUQNFpUhg5H-AqKt1ImX0pg3AWEKSIevFm_J4jsBgzwib5-xDb1e0uh7GN4K32xvBnKD_TpRVByFbwoN2Kbfuc4FjvyiHvp1QP35gLzktNudQdb75wng4ln0_Lmj0QHBd8vLdiw-tu6N6b_vPto3vpG7DONUApkhLRW0LJQ0JCG2RUgtJeoiEfuXcIFsBbzZVx5FTiQkcZjNLRq4o93bZX6ngq0wzld_wnj1ey-gO_8TrQ</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Local Ergodic Theorems for C0-Semigroups</title><source>arXiv.org</source><creator>Tajmouati, Abdelaziz ; Barki, Fatih</creator><creatorcontrib>Tajmouati, Abdelaziz ; Barki, Fatih</creatorcontrib><description>Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on
the Banach space ${X}$ into itself and let $A$ be their infinitesimal
generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$
does not have the single valued extension property, which implies that $A$ must
have a nonempty interior of the point spectrum. Furthermore, we introduce the
local mean ergodic for $C_0$-semigroup $T(t)$ at a vector $x\in X$ and we
establish some conditions implying that $T(t)$ is a local mean ergodic at $x$.</description><identifier>DOI: 10.48550/arxiv.1912.10947</identifier><language>eng</language><subject>Mathematics - Functional Analysis</subject><creationdate>2019-12</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1912.10947$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1912.10947$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Tajmouati, Abdelaziz</creatorcontrib><creatorcontrib>Barki, Fatih</creatorcontrib><title>Local Ergodic Theorems for C0-Semigroups</title><description>Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on
the Banach space ${X}$ into itself and let $A$ be their infinitesimal
generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$
does not have the single valued extension property, which implies that $A$ must
have a nonempty interior of the point spectrum. Furthermore, we introduce the
local mean ergodic for $C_0$-semigroup $T(t)$ at a vector $x\in X$ and we
establish some conditions implying that $T(t)$ is a local mean ergodic at $x$.</description><subject>Mathematics - Functional Analysis</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzrlqw0AUQNFpUhg5H-AqKt1ImX0pg3AWEKSIevFm_J4jsBgzwib5-xDb1e0uh7GN4K32xvBnKD_TpRVByFbwoN2Kbfuc4FjvyiHvp1QP35gLzktNudQdb75wng4ln0_Lmj0QHBd8vLdiw-tu6N6b_vPto3vpG7DONUApkhLRW0LJQ0JCG2RUgtJeoiEfuXcIFsBbzZVx5FTiQkcZjNLRq4o93bZX6ngq0wzld_wnj1ey-gO_8TrQ</recordid><startdate>20191223</startdate><enddate>20191223</enddate><creator>Tajmouati, Abdelaziz</creator><creator>Barki, Fatih</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20191223</creationdate><title>Local Ergodic Theorems for C0-Semigroups</title><author>Tajmouati, Abdelaziz ; Barki, Fatih</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-afcbf31b86fe209cefe692b31fcd2e5f8b087ea6aa8640357f73c014b29534b83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Functional Analysis</topic><toplevel>online_resources</toplevel><creatorcontrib>Tajmouati, Abdelaziz</creatorcontrib><creatorcontrib>Barki, Fatih</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Tajmouati, Abdelaziz</au><au>Barki, Fatih</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Local Ergodic Theorems for C0-Semigroups</atitle><date>2019-12-23</date><risdate>2019</risdate><abstract>Let $\{T(t)\}_{t\geq 0}$ be a $C_0$-semigroup of bounded linear operators on
the Banach space ${X}$ into itself and let $A$ be their infinitesimal
generator. In this paper, we show that if $T(t)$ is uniformly ergodic, then $A$
does not have the single valued extension property, which implies that $A$ must
have a nonempty interior of the point spectrum. Furthermore, we introduce the
local mean ergodic for $C_0$-semigroup $T(t)$ at a vector $x\in X$ and we
establish some conditions implying that $T(t)$ is a local mean ergodic at $x$.</abstract><doi>10.48550/arxiv.1912.10947</doi><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext_linktorsrc |
| identifier | DOI: 10.48550/arxiv.1912.10947 |
| ispartof | |
| issn | |
| language | eng |
| recordid | cdi_arxiv_primary_1912_10947 |
| source | arXiv.org |
| subjects | Mathematics - Functional Analysis |
| title | Local Ergodic Theorems for C0-Semigroups |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T12%3A03%3A46IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Local%20Ergodic%20Theorems%20for%20C0-Semigroups&rft.au=Tajmouati,%20Abdelaziz&rft.date=2019-12-23&rft_id=info:doi/10.48550/arxiv.1912.10947&rft_dat=%3Carxiv_GOX%3E1912_10947%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |