The isomorphism relation for separable $C*$-algebras
نویسندگان
چکیده
منابع مشابه
The Isomorphism Relation for Separable C*-algebras
We prove that the isomorphism relation for separable C∗-algebras, and also the relations of complete and n-isometry for operator spaces and systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.
متن کاملThe spatial isomorphism problem for close separable nuclear C*-algebras.
The Kadison-Kastler problem asks whether close C*-algebras on a Hilbert space must be spatially isomorphic. We establish this when one of the algebras is separable and nuclear. We also apply our methods to the study of near inclusions of C*-algebras.
متن کاملThe Completeness of the Isomorphism Relation for Countable Boolean Algebras
We show that the isomorphism relation for countable Boolean algebras is Borel complete, i.e., the isomorphism relation for arbitrary countable structures is Borel reducible to that for countable Boolean algebras. This implies that Ketonen’s classification of countable Boolean algebras is optimal in the sense that the kind of objects used for the complete invariants cannot be improved in an esse...
متن کاملInjective Envelopes of Separable C * -algebras
Characterisations of those separable C∗-algebras that have type I injective envelopes or W∗-algebra injective envelopes are presented. An operator system I is injective if for every inclusion E ⊂ F of operator systems each completely positive linear map ω : E → I has a completely positive extension to F . An injective envelope of an operator system E is an injective operator system I such that ...
متن کاملThe Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras
Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 2013
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.2013.v20.n6.a6