EXISTENCE OF FELLER COCYCLES ON A C-ALGEBRA
The quantum stochastic differential equation dkt = kt ∘ θαβdΛβα(t) is considered on a unital C*-algebra, with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for the existence of a completely positive contractive solution are shown to be sufficient. It is...
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| Veröffentlicht in: | The Bulletin of the London Mathematical Society 2001-09, Vol.33 (5), p.613-621 |
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| container_title | The Bulletin of the London Mathematical Society |
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| creator | LINDSAY, J. MARTIN WILLS, STEPHEN J. |
| description | The quantum stochastic differential equation dkt = kt ∘
θαβdΛβα(t)
is considered on a unital C*-algebra,
with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for
the existence of a completely positive contractive solution are shown to be sufficient. It is known that
for completely positive contraction processes, k satisfies such an equation if and only if k is a
regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology
if the algebra is thought of as a non-commutative topological space. |
| doi_str_mv | 10.1112/S0024609301008128 |
| format | Article |
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θαβdΛβα(t)
is considered on a unital C*-algebra,
with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for
the existence of a completely positive contractive solution are shown to be sufficient. It is known that
for completely positive contraction processes, k satisfies such an equation if and only if k is a
regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology
if the algebra is thought of as a non-commutative topological space.</description><identifier>ISSN: 0024-6093</identifier><identifier>EISSN: 1469-2120</identifier><identifier>DOI: 10.1112/S0024609301008128</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>NOTES AND PAPERS</subject><ispartof>The Bulletin of the London Mathematical Society, 2001-09, Vol.33 (5), p.613-621</ispartof><rights>The London Mathematical Society 2001</rights><rights>2001 London Mathematical Society</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3733-306b51252aabb9a6353cbb1984576983fb611c314d63a53d4ac914b018ce98b43</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1112%2FS0024609301008128$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1112%2FS0024609301008128$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>LINDSAY, J. MARTIN</creatorcontrib><creatorcontrib>WILLS, STEPHEN J.</creatorcontrib><title>EXISTENCE OF FELLER COCYCLES ON A C-ALGEBRA</title><title>The Bulletin of the London Mathematical Society</title><addtitle>Bull. Lond. Math. Soc</addtitle><description>The quantum stochastic differential equation dkt = kt ∘
θαβdΛβα(t)
is considered on a unital C*-algebra,
with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for
the existence of a completely positive contractive solution are shown to be sufficient. It is known that
for completely positive contraction processes, k satisfies such an equation if and only if k is a
regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology
if the algebra is thought of as a non-commutative topological space.</description><subject>NOTES AND PAPERS</subject><issn>0024-6093</issn><issn>1469-2120</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><recordid>eNqFkEFLw0AUhBdRsFZ_gLfcJbpv32aTPabLtimsDTQVqpdlN00ltbWSKNp_b0qLF0FPc5j5HjOPkGugtwDA7gpKGRdUIgVKE2DJCekBFzJkwOgp6e3tcO-fk4u2XVEKSGPokRs9HxczPVE6yIfBUBujp4HK1aMyugjySZAGKkzNSA-m6SU5W7p1W10dtU8ehnqmstDko7FKTVhijBgiFT4CFjHnvJdOYISl9yATHsVCJrj0AqBE4AuBLsIFd6UE7ikkZSUTz7FP4HC3bLZt21RL-9bUG9fsLFC7X2t_re2Y-MB81utq9z9gB-a-oAKwI8MDWbfv1dcP6ZoXK2KMI5vNnyyfmYhlKrNZl8djO7fxTb14ruxq-9G8dh_5o983wIduRw</recordid><startdate>200109</startdate><enddate>200109</enddate><creator>LINDSAY, J. MARTIN</creator><creator>WILLS, STEPHEN J.</creator><general>Cambridge University Press</general><general>Oxford University Press</general><scope>BSCLL</scope><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>200109</creationdate><title>EXISTENCE OF FELLER COCYCLES ON A C-ALGEBRA</title><author>LINDSAY, J. MARTIN ; WILLS, STEPHEN J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3733-306b51252aabb9a6353cbb1984576983fb611c314d63a53d4ac914b018ce98b43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2001</creationdate><topic>NOTES AND PAPERS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>LINDSAY, J. MARTIN</creatorcontrib><creatorcontrib>WILLS, STEPHEN J.</creatorcontrib><collection>Istex</collection><collection>CrossRef</collection><jtitle>The Bulletin of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>LINDSAY, J. MARTIN</au><au>WILLS, STEPHEN J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>EXISTENCE OF FELLER COCYCLES ON A C-ALGEBRA</atitle><jtitle>The Bulletin of the London Mathematical Society</jtitle><addtitle>Bull. Lond. Math. Soc</addtitle><date>2001-09</date><risdate>2001</risdate><volume>33</volume><issue>5</issue><spage>613</spage><epage>621</epage><pages>613-621</pages><issn>0024-6093</issn><eissn>1469-2120</eissn><abstract>The quantum stochastic differential equation dkt = kt ∘
θαβdΛβα(t)
is considered on a unital C*-algebra,
with separable noise dimension space. Necessary conditions on the matrix of bounded linear maps θ for
the existence of a completely positive contractive solution are shown to be sufficient. It is known that
for completely positive contraction processes, k satisfies such an equation if and only if k is a
regular Markovian cocycle. ‘Feller’ refers to an invariance condition analogous to probabilistic terminology
if the algebra is thought of as a non-commutative topological space.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1112/S0024609301008128</doi><tpages>9</tpages></addata></record> |
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| identifier | ISSN: 0024-6093 |
| ispartof | The Bulletin of the London Mathematical Society, 2001-09, Vol.33 (5), p.613-621 |
| issn | 0024-6093 1469-2120 |
| language | eng |
| recordid | cdi_crossref_primary_10_1112_S0024609301008128 |
| source | Wiley Journals; Alma/SFX Local Collection |
| subjects | NOTES AND PAPERS |
| title | EXISTENCE OF FELLER COCYCLES ON A C-ALGEBRA |
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