A Hilbert $C^*$-module not anti-isomorphic to itself
نویسندگان
چکیده
منابع مشابه
A Hilbert C∗-module Not Anti-isomorphic to Itself
We study the complexification of real Hilbert C∗-modules over real C∗-algebras. We give an example of a Hilbert Ac-module that is not the complexification of any Hilbert A-module, where A is a real C∗-algebra.
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In this paper, we state some results on product of operators with closed ranges and we solve the operator equation $TXS^*-SX^*T^*= A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $TS = 1$. Furthermore, by using some block operator matrix techniques, we nd explicit solution of the operator equation $TXS^*-SX^*T^*= A$.
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We show that every infinite-dimensional commutative unital C∗-algebra has a Hilbert C∗-module admitting no frames. In particular, this shows that Kasparov’s stabilization theorem for countably generated Hilbert C∗-modules can not be extended to arbitrary Hilbert C∗-modules.
متن کاملWhat is a Hilbert C ∗-module? ∗
In this paper we view some fundamentals of the theory of Hilbert C-modules and examine some ways in which Hilbert C-modules differ from Hilbert spaces. ∗2000 Mathematics Subject Classification. 46L08.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-06-08474-7