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Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras
Let M be a von Neumann algebra with no central summands of type I 1 . Assume that Φ : M → M is a surjective map and Φ ( I ) is an unitary operator. It is shown that Φ is strong bi-skew commutativity preserving (that is, Φ satisfies Φ ( A ) Φ ( B ) ∗ - Φ ( B ) Φ ( A ) ∗ = A B ∗ - B A ∗ for all A , B...
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| Published in: | Bulletin of the Iranian Mathematical Society 2023-04, Vol.49 (2), Article 15 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_title | Bulletin of the Iranian Mathematical Society |
| container_volume | 49 |
| creator | Qi, Xiaofei Chen, Shaobo |
| description | Let
M
be a von Neumann algebra with no central summands of type
I
1
. Assume that
Φ
:
M
→
M
is a surjective map and
Φ
(
I
)
is an unitary operator. It is shown that
Φ
is strong bi-skew commutativity preserving (that is,
Φ
satisfies
Φ
(
A
)
Φ
(
B
)
∗
-
Φ
(
B
)
Φ
(
A
)
∗
=
A
B
∗
-
B
A
∗
for all
A
,
B
∈
M
) if and only if there exists a self-adjoint central operator
Z
∈
M
with
Z
2
=
I
such that
Φ
(
A
)
=
Z
A
Φ
(
I
)
for all
A
∈
M
. The strong bi-skew commutativity preserving maps on prime algebras with involution are also characterized. |
| doi_str_mv | 10.1007/s41980-023-00759-7 |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s41980_023_00759_7</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s41980_023_00759_7</sourcerecordid><originalsourceid>FETCH-LOGICAL-c281t-13dc438bbc5b251215d071a2c74d65b9690d73151dfed300471138eb9e13363</originalsourceid><addsrcrecordid>eNp9kMtOwzAQRS0EElXpD7DKDxhm_IidZSmPIpWHVBbsLDtxq0CTVHYa1L_HENYsRjMj3TMaHUIuEa4QQF1HgYUGCozTtMqCqhMyQcUl1RLlaZoBFYUc3s_JLMbagRAMtRZiQm7XfejabXZT0_jpv7JF1zSH3vb1UPfH7DX46MNQp8CT3cesa7Mh1bM_NLZts_lu612w8YKcbewu-tlfn5L1_d3bYklXLw-Pi_mKlkxjT5FXpeDauVI6JpGhrEChZaUSVS5dkRdQKY4Sq42vOIBQiFx7V3jkPOdTwsarZehiDH5j9qFubDgaBPMjwowiTBJhfkUYlSA-QjGF260P5qM7hDZ9-R_1DTgsYDA</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras</title><source>Springer Link</source><creator>Qi, Xiaofei ; Chen, Shaobo</creator><creatorcontrib>Qi, Xiaofei ; Chen, Shaobo</creatorcontrib><description>Let
M
be a von Neumann algebra with no central summands of type
I
1
. Assume that
Φ
:
M
→
M
is a surjective map and
Φ
(
I
)
is an unitary operator. It is shown that
Φ
is strong bi-skew commutativity preserving (that is,
Φ
satisfies
Φ
(
A
)
Φ
(
B
)
∗
-
Φ
(
B
)
Φ
(
A
)
∗
=
A
B
∗
-
B
A
∗
for all
A
,
B
∈
M
) if and only if there exists a self-adjoint central operator
Z
∈
M
with
Z
2
=
I
such that
Φ
(
A
)
=
Z
A
Φ
(
I
)
for all
A
∈
M
. The strong bi-skew commutativity preserving maps on prime algebras with involution are also characterized.</description><identifier>ISSN: 1017-060X</identifier><identifier>EISSN: 1735-8515</identifier><identifier>DOI: 10.1007/s41980-023-00759-7</identifier><language>eng</language><publisher>Singapore: Springer Nature Singapore</publisher><subject>Mathematics ; Mathematics and Statistics ; Original Paper</subject><ispartof>Bulletin of the Iranian Mathematical Society, 2023-04, Vol.49 (2), Article 15</ispartof><rights>The Author(s) under exclusive licence to Iranian Mathematical Society 2023. 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-c281t-13dc438bbc5b251215d071a2c74d65b9690d73151dfed300471138eb9e13363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Qi, Xiaofei</creatorcontrib><creatorcontrib>Chen, Shaobo</creatorcontrib><title>Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras</title><title>Bulletin of the Iranian Mathematical Society</title><addtitle>Bull. Iran. Math. Soc</addtitle><description>Let
M
be a von Neumann algebra with no central summands of type
I
1
. Assume that
Φ
:
M
→
M
is a surjective map and
Φ
(
I
)
is an unitary operator. It is shown that
Φ
is strong bi-skew commutativity preserving (that is,
Φ
satisfies
Φ
(
A
)
Φ
(
B
)
∗
-
Φ
(
B
)
Φ
(
A
)
∗
=
A
B
∗
-
B
A
∗
for all
A
,
B
∈
M
) if and only if there exists a self-adjoint central operator
Z
∈
M
with
Z
2
=
I
such that
Φ
(
A
)
=
Z
A
Φ
(
I
)
for all
A
∈
M
. The strong bi-skew commutativity preserving maps on prime algebras with involution are also characterized.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><issn>1017-060X</issn><issn>1735-8515</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EElXpD7DKDxhm_IidZSmPIpWHVBbsLDtxq0CTVHYa1L_HENYsRjMj3TMaHUIuEa4QQF1HgYUGCozTtMqCqhMyQcUl1RLlaZoBFYUc3s_JLMbagRAMtRZiQm7XfejabXZT0_jpv7JF1zSH3vb1UPfH7DX46MNQp8CT3cesa7Mh1bM_NLZts_lu612w8YKcbewu-tlfn5L1_d3bYklXLw-Pi_mKlkxjT5FXpeDauVI6JpGhrEChZaUSVS5dkRdQKY4Sq42vOIBQiFx7V3jkPOdTwsarZehiDH5j9qFubDgaBPMjwowiTBJhfkUYlSA-QjGF260P5qM7hDZ9-R_1DTgsYDA</recordid><startdate>20230401</startdate><enddate>20230401</enddate><creator>Qi, Xiaofei</creator><creator>Chen, Shaobo</creator><general>Springer Nature Singapore</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230401</creationdate><title>Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras</title><author>Qi, Xiaofei ; Chen, Shaobo</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c281t-13dc438bbc5b251215d071a2c74d65b9690d73151dfed300471138eb9e13363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Qi, Xiaofei</creatorcontrib><creatorcontrib>Chen, Shaobo</creatorcontrib><collection>CrossRef</collection><jtitle>Bulletin of the Iranian Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Qi, Xiaofei</au><au>Chen, Shaobo</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras</atitle><jtitle>Bulletin of the Iranian Mathematical Society</jtitle><stitle>Bull. Iran. Math. Soc</stitle><date>2023-04-01</date><risdate>2023</risdate><volume>49</volume><issue>2</issue><artnum>15</artnum><issn>1017-060X</issn><eissn>1735-8515</eissn><abstract>Let
M
be a von Neumann algebra with no central summands of type
I
1
. Assume that
Φ
:
M
→
M
is a surjective map and
Φ
(
I
)
is an unitary operator. It is shown that
Φ
is strong bi-skew commutativity preserving (that is,
Φ
satisfies
Φ
(
A
)
Φ
(
B
)
∗
-
Φ
(
B
)
Φ
(
A
)
∗
=
A
B
∗
-
B
A
∗
for all
A
,
B
∈
M
) if and only if there exists a self-adjoint central operator
Z
∈
M
with
Z
2
=
I
such that
Φ
(
A
)
=
Z
A
Φ
(
I
)
for all
A
∈
M
. The strong bi-skew commutativity preserving maps on prime algebras with involution are also characterized.</abstract><cop>Singapore</cop><pub>Springer Nature Singapore</pub><doi>10.1007/s41980-023-00759-7</doi></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1017-060X |
| ispartof | Bulletin of the Iranian Mathematical Society, 2023-04, Vol.49 (2), Article 15 |
| issn | 1017-060X 1735-8515 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s41980_023_00759_7 |
| source | Springer Link |
| subjects | Mathematics Mathematics and Statistics Original Paper |
| title | Strong Bi-skew Commutativity Preserving Maps on von Neumann Algebras |
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