On compact and Fredholm operators over $C^*$-algebras and a new topology in the space of compact operatorsстатья
Информация о цитировании статьи получена из
Web of Science
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 27 мая 2015 г.
Аннотация:It is shown that the class of Fredholm operators over an arbitrary
unital C∗–algebra, which may not admit adjoint ones, can be extended
in such a way that this class of compact operators, used in the definition
of the class of Fredholm operators, contains compact operators both with
and without existence of adjoint ones. The main property of this new
class is that a Fredholm operator which may not admit an adjoint one
has a decomposition into a direct sum of an isomorphism and a finitely
generated operator.
In the space of compact operators in the Hilbert space a new IM-
topology is defined. In the case when the C∗–algebra is a commutative
algebra of continuous functions on a compact space the IM-topology fully
describe the set of compact operators over the C∗–algebra without as-
sumption of existence bounded adjoint operators over the algebra.