The Regularity and Uniform Positivity of the Range of Orthogonal Projections
Given two orthogonal projections P , Q ∈ B ( H ) , let T = P Q and R ( T ) ⊥ ∩ N ( T ) = { 0 } , we characterize symmetries J such that ( J T ) ∗ = J T and J T ≥ 0 , where ( J T ) ∗ = J T if and only if P J = J Q . Furthermore, we study the regularity and uniform positivity of R ( P ) and R ( Q ) ....
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| Veröffentlicht in: | Complex analysis and operator theory 2024-11, Vol.18 (8), Article 174 |
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| container_title | Complex analysis and operator theory |
| container_volume | 18 |
| creator | Zhang, Lulu Hai, Guojun |
| description | Given two orthogonal projections
P
,
Q
∈
B
(
H
)
, let
T
=
P
Q
and
R
(
T
)
⊥
∩
N
(
T
)
=
{
0
}
, we characterize symmetries
J
such that
(
J
T
)
∗
=
J
T
and
J
T
≥
0
, where
(
J
T
)
∗
=
J
T
if and only if
P
J
=
J
Q
. Furthermore, we study the regularity and uniform positivity of
R
(
P
)
and
R
(
Q
)
. |
| doi_str_mv | 10.1007/s11785-024-01621-2 |
| format | Article |
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P
,
Q
∈
B
(
H
)
, let
T
=
P
Q
and
R
(
T
)
⊥
∩
N
(
T
)
=
{
0
}
, we characterize symmetries
J
such that
(
J
T
)
∗
=
J
T
and
J
T
≥
0
, where
(
J
T
)
∗
=
J
T
if and only if
P
J
=
J
Q
. Furthermore, we study the regularity and uniform positivity of
R
(
P
)
and
R
(
Q
)
.</description><identifier>ISSN: 1661-8254</identifier><identifier>EISSN: 1661-8262</identifier><identifier>DOI: 10.1007/s11785-024-01621-2</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Mathematics ; Mathematics and Statistics ; Operator Theory ; Regularity</subject><ispartof>Complex analysis and operator theory, 2024-11, Vol.18 (8), Article 174</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-538dcef9b2fb2edfcd8233549d172d310240b7d88be71beb08080306dc3aca93</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11785-024-01621-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11785-024-01621-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27903,27904,41467,42536,51297</link.rule.ids></links><search><creatorcontrib>Zhang, Lulu</creatorcontrib><creatorcontrib>Hai, Guojun</creatorcontrib><title>The Regularity and Uniform Positivity of the Range of Orthogonal Projections</title><title>Complex analysis and operator theory</title><addtitle>Complex Anal. Oper. Theory</addtitle><description>Given two orthogonal projections
P
,
Q
∈
B
(
H
)
, let
T
=
P
Q
and
R
(
T
)
⊥
∩
N
(
T
)
=
{
0
}
, we characterize symmetries
J
such that
(
J
T
)
∗
=
J
T
and
J
T
≥
0
, where
(
J
T
)
∗
=
J
T
if and only if
P
J
=
J
Q
. Furthermore, we study the regularity and uniform positivity of
R
(
P
)
and
R
(
Q
)
.</description><subject>Analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Operator Theory</subject><subject>Regularity</subject><issn>1661-8254</issn><issn>1661-8262</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9UE1LAzEQDaJgrf4BTwueo5NkN5s9SvELChap55DNR7ul3dQkFfrvzbqiN5nDfPDem5mH0DWBWwJQ30VCalFhoCUGwinB9ARNCOcEC8rp6W9dlefoIsYNAIe6aSZovlzb4s2uDlsVunQsVG-K975zPuyKhY9d6j6HsXdFGoCqX9mheQ1p7Ve-V9tiEfzG6tT5Pl6iM6e20V795ClaPj4sZ894_vr0MrufY00BEq6YMNq6pqWupdY4bQRlrCobQ2pqGMlfQFsbIVpbk9a2IHIw4EYzpVXDpuhmlN0H_3GwMcmNP4R8S5SMkIZXDEqWUXRE6eBjDNbJfeh2KhwlATmYJkfTZF4nv02TNJPYSIoZnH8Nf9L_sL4AqRFvWg</recordid><startdate>20241101</startdate><enddate>20241101</enddate><creator>Zhang, Lulu</creator><creator>Hai, Guojun</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20241101</creationdate><title>The Regularity and Uniform Positivity of the Range of Orthogonal Projections</title><author>Zhang, Lulu ; Hai, Guojun</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-538dcef9b2fb2edfcd8233549d172d310240b7d88be71beb08080306dc3aca93</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Operator Theory</topic><topic>Regularity</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhang, Lulu</creatorcontrib><creatorcontrib>Hai, Guojun</creatorcontrib><collection>CrossRef</collection><jtitle>Complex analysis and operator theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhang, Lulu</au><au>Hai, Guojun</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The Regularity and Uniform Positivity of the Range of Orthogonal Projections</atitle><jtitle>Complex analysis and operator theory</jtitle><stitle>Complex Anal. Oper. Theory</stitle><date>2024-11-01</date><risdate>2024</risdate><volume>18</volume><issue>8</issue><artnum>174</artnum><issn>1661-8254</issn><eissn>1661-8262</eissn><abstract>Given two orthogonal projections
P
,
Q
∈
B
(
H
)
, let
T
=
P
Q
and
R
(
T
)
⊥
∩
N
(
T
)
=
{
0
}
, we characterize symmetries
J
such that
(
J
T
)
∗
=
J
T
and
J
T
≥
0
, where
(
J
T
)
∗
=
J
T
if and only if
P
J
=
J
Q
. Furthermore, we study the regularity and uniform positivity of
R
(
P
)
and
R
(
Q
)
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s11785-024-01621-2</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1661-8254 |
| ispartof | Complex analysis and operator theory, 2024-11, Vol.18 (8), Article 174 |
| issn | 1661-8254 1661-8262 |
| language | eng |
| recordid | cdi_proquest_journals_3119653043 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Analysis Mathematics Mathematics and Statistics Operator Theory Regularity |
| title | The Regularity and Uniform Positivity of the Range of Orthogonal Projections |
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