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A Note on Derivations on the Algebra of Operators in Hilbert C-Modules
Let M be a Hilbert C *-module on a C *-algebra A and let E n d A ( M ) be the algebra of all operators on M . In this paper, first the continuity of A -module homomorphism derivations on E n d A ( M ) is investigated. We give some sufficient conditions on which every derivation on E n d A ( M ) is i...
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| Published in: | Mediterranean journal of mathematics 2016-06, Vol.13 (3), p.1167-1175 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3 |
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| cites | cdi_FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3 |
| container_end_page | 1175 |
| container_issue | 3 |
| container_start_page | 1167 |
| container_title | Mediterranean journal of mathematics |
| container_volume | 13 |
| creator | Kafi Moghadam, Mostafa Miri, M. Janfada, A. R. |
| description | Let
M
be a Hilbert
C
*-module on a
C
*-algebra
A
and let
E
n
d
A
(
M
)
be the algebra of all operators on
M
. In this paper, first the continuity of
A
-module homomorphism derivations on
E
n
d
A
(
M
)
is investigated. We give some sufficient conditions on which every derivation on
E
n
d
A
(
M
)
is inner. Next, we study approximately innerness of derivations on
E
n
d
A
(
M
)
for a
σ
-unital
C
*-algebra
A
and full Hilbert
A
-module
M
. Finally, we show that every bounded linear mapping on
E
n
d
A
(
M
)
which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation. |
| doi_str_mv | 10.1007/s00009-015-0538-y |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s00009_015_0538_y</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s00009_015_0538_y</sourcerecordid><originalsourceid>FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3</originalsourceid><addsrcrecordid>eNp9kMFOwzAMhiMEEmPwANzyAgE7Sbv0OA3GkIBd4BwljTs6lWZKOqS9PZ2GOOKL_Uv-LOtj7BbhDgFm9xnGqgRgIaBQRhzO2ATLEkShC33-N-vykl3lvAWQFSo5Ycs5f4sD8djzB0rttxva2OdjHD6Jz7sN-eR4bPh6R8kNMWXe9nzVdp7SwBfiNYZ9R_maXTSuy3Tz26fsY_n4vliJl_XT82L-ImppzCAC1dr5gA0ZNIECGEXgJClXO_RYgfS-1HU1U0FV5UxrRJJIJkhdB98ENWV4ulunmHOixu5S--XSwSLYowh7EmFHEfYowh5GRp6YPO72G0p2G_epH9_8B_oB0QphQw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A Note on Derivations on the Algebra of Operators in Hilbert C-Modules</title><source>Springer Nature</source><creator>Kafi Moghadam, Mostafa ; Miri, M. ; Janfada, A. R.</creator><creatorcontrib>Kafi Moghadam, Mostafa ; Miri, M. ; Janfada, A. R.</creatorcontrib><description>Let
M
be a Hilbert
C
*-module on a
C
*-algebra
A
and let
E
n
d
A
(
M
)
be the algebra of all operators on
M
. In this paper, first the continuity of
A
-module homomorphism derivations on
E
n
d
A
(
M
)
is investigated. We give some sufficient conditions on which every derivation on
E
n
d
A
(
M
)
is inner. Next, we study approximately innerness of derivations on
E
n
d
A
(
M
)
for a
σ
-unital
C
*-algebra
A
and full Hilbert
A
-module
M
. Finally, we show that every bounded linear mapping on
E
n
d
A
(
M
)
which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation.</description><identifier>ISSN: 1660-5446</identifier><identifier>EISSN: 1660-5454</identifier><identifier>DOI: 10.1007/s00009-015-0538-y</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Mathematics ; Mathematics and Statistics</subject><ispartof>Mediterranean journal of mathematics, 2016-06, Vol.13 (3), p.1167-1175</ispartof><rights>Springer Basel 2015</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3</citedby><cites>FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Kafi Moghadam, Mostafa</creatorcontrib><creatorcontrib>Miri, M.</creatorcontrib><creatorcontrib>Janfada, A. R.</creatorcontrib><title>A Note on Derivations on the Algebra of Operators in Hilbert C-Modules</title><title>Mediterranean journal of mathematics</title><addtitle>Mediterr. J. Math</addtitle><description>Let
M
be a Hilbert
C
*-module on a
C
*-algebra
A
and let
E
n
d
A
(
M
)
be the algebra of all operators on
M
. In this paper, first the continuity of
A
-module homomorphism derivations on
E
n
d
A
(
M
)
is investigated. We give some sufficient conditions on which every derivation on
E
n
d
A
(
M
)
is inner. Next, we study approximately innerness of derivations on
E
n
d
A
(
M
)
for a
σ
-unital
C
*-algebra
A
and full Hilbert
A
-module
M
. Finally, we show that every bounded linear mapping on
E
n
d
A
(
M
)
which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation.</description><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>1660-5446</issn><issn>1660-5454</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp9kMFOwzAMhiMEEmPwANzyAgE7Sbv0OA3GkIBd4BwljTs6lWZKOqS9PZ2GOOKL_Uv-LOtj7BbhDgFm9xnGqgRgIaBQRhzO2ATLEkShC33-N-vykl3lvAWQFSo5Ycs5f4sD8djzB0rttxva2OdjHD6Jz7sN-eR4bPh6R8kNMWXe9nzVdp7SwBfiNYZ9R_maXTSuy3Tz26fsY_n4vliJl_XT82L-ImppzCAC1dr5gA0ZNIECGEXgJClXO_RYgfS-1HU1U0FV5UxrRJJIJkhdB98ENWV4ulunmHOixu5S--XSwSLYowh7EmFHEfYowh5GRp6YPO72G0p2G_epH9_8B_oB0QphQw</recordid><startdate>20160601</startdate><enddate>20160601</enddate><creator>Kafi Moghadam, Mostafa</creator><creator>Miri, M.</creator><creator>Janfada, A. R.</creator><general>Springer International Publishing</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20160601</creationdate><title>A Note on Derivations on the Algebra of Operators in Hilbert C-Modules</title><author>Kafi Moghadam, Mostafa ; Miri, M. ; Janfada, A. R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c288t-dec4abd1fe818ded083e0a2e3aca1b1902bb64c973d39674411e21e8d24cdbfd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kafi Moghadam, Mostafa</creatorcontrib><creatorcontrib>Miri, M.</creatorcontrib><creatorcontrib>Janfada, A. R.</creatorcontrib><collection>CrossRef</collection><jtitle>Mediterranean journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kafi Moghadam, Mostafa</au><au>Miri, M.</au><au>Janfada, A. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Note on Derivations on the Algebra of Operators in Hilbert C-Modules</atitle><jtitle>Mediterranean journal of mathematics</jtitle><stitle>Mediterr. J. Math</stitle><date>2016-06-01</date><risdate>2016</risdate><volume>13</volume><issue>3</issue><spage>1167</spage><epage>1175</epage><pages>1167-1175</pages><issn>1660-5446</issn><eissn>1660-5454</eissn><abstract>Let
M
be a Hilbert
C
*-module on a
C
*-algebra
A
and let
E
n
d
A
(
M
)
be the algebra of all operators on
M
. In this paper, first the continuity of
A
-module homomorphism derivations on
E
n
d
A
(
M
)
is investigated. We give some sufficient conditions on which every derivation on
E
n
d
A
(
M
)
is inner. Next, we study approximately innerness of derivations on
E
n
d
A
(
M
)
for a
σ
-unital
C
*-algebra
A
and full Hilbert
A
-module
M
. Finally, we show that every bounded linear mapping on
E
n
d
A
(
M
)
which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00009-015-0538-y</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1660-5446 |
| ispartof | Mediterranean journal of mathematics, 2016-06, Vol.13 (3), p.1167-1175 |
| issn | 1660-5446 1660-5454 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s00009_015_0538_y |
| source | Springer Nature |
| subjects | Mathematics Mathematics and Statistics |
| title | A Note on Derivations on the Algebra of Operators in Hilbert C-Modules |
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