The Calkin algebra is not countably homogeneous
نویسندگان
چکیده
منابع مشابه
Asymptotic homomorphisms into the Calkin algebra ∗
Let A be a separable C∗-algebra and let B be a stable C∗-algebra with a strictly positive element. We consider the (semi)group Ext(A,B) (resp. Ext(A,B)) of homotopy classes of asymptotic (resp. of genuine) homomorphisms from A to the corona algebra M(B)/B and the natural map i : Ext(A,B) −→ Ext(A,B). We show that if A is a suspension then Ext(A,B) coincides with E-theory of Connes and Higson an...
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It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...
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We prove that it is relatively consistent with the usual axioms of mathematics that all automorphisms of the Calkin algebra are inner. Together with a 2006 Phillips–Weaver construction of an outer automorphism using the Continuum Hypothesis, this gives a complete solution to a 1977 problem of Brown–Douglas–Fillmore. We also give a simpler and self-contained proof of the Phillips–Weaver result. ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13137