UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS
It is shown that an unbounded *-derivation δ of a unital commutative C*-algebra A is quasi well-behaved if and only if there is a dense open subset U of the spectrum of A such that, for any f in the domain of δ, δ(f) vanishes at any point of U where f attains its norm. An example is given to show th...
| Autor principal: | |
|---|---|
| Format: | Journal article |
| Idioma: | English |
| Publicat: |
Springer-Verlag
1978
|
| _version_ | 1826272707888545792 |
|---|---|
| author | Batty, C |
| author_facet | Batty, C |
| author_sort | Batty, C |
| collection | OXFORD |
| description | It is shown that an unbounded *-derivation δ of a unital commutative C*-algebra A is quasi well-behaved if and only if there is a dense open subset U of the spectrum of A such that, for any f in the domain of δ, δ(f) vanishes at any point of U where f attains its norm. An example is given to show that even if δ is closed it need not be quasi well-behaved. This answers negatively a question posed by Sakai for arbitrary C*-algebras. It is also shown that there are no-zero closed derivations on A if the spectrum of A contains a dense open totally disconnected subset. © 1978 Springer-Verlag. |
| first_indexed | 2024-03-06T22:16:51Z |
| format | Journal article |
| id | oxford-uuid:53a7d03b-c721-4bd7-91c9-f8b33e808dd5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:16:51Z |
| publishDate | 1978 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | oxford-uuid:53a7d03b-c721-4bd7-91c9-f8b33e808dd52022-03-26T16:33:10ZUNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRASJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:53a7d03b-c721-4bd7-91c9-f8b33e808dd5EnglishSymplectic Elements at OxfordSpringer-Verlag1978Batty, CIt is shown that an unbounded *-derivation δ of a unital commutative C*-algebra A is quasi well-behaved if and only if there is a dense open subset U of the spectrum of A such that, for any f in the domain of δ, δ(f) vanishes at any point of U where f attains its norm. An example is given to show that even if δ is closed it need not be quasi well-behaved. This answers negatively a question posed by Sakai for arbitrary C*-algebras. It is also shown that there are no-zero closed derivations on A if the spectrum of A contains a dense open totally disconnected subset. © 1978 Springer-Verlag. |
| spellingShingle | Batty, C UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title | UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title_full | UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title_fullStr | UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title_full_unstemmed | UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title_short | UNBOUNDED DERIVATIONS OF COMMUTATIVE CSTAR-ALGEBRAS |
| title_sort | unbounded derivations of commutative cstar algebras |
| work_keys_str_mv | AT battyc unboundedderivationsofcommutativecstaralgebras |