A Characterization of Compact Groups
نویسندگان
چکیده
منابع مشابه
A characterization of compact quantum groups through second duals
A locally compact group G is compact if and only if L(G) is an ideal in L(G). On the other hand, the Fourier algebra A(G) of G is an ideal in A(G)∗∗ if and only if G is discrete. We show that both results are special cases of one general theorem on locally compact quantum groups in the sense of J. Kustermans and S. Vaes: a von Neumann algebraic quantum group (M,Γ) is compact if and only if M∗ i...
متن کاملOn component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملBracket Products on Locally Compact Abelian Groups
We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملA characterization of simple $K_4$-groups of type $L_2(q)$ and their automorphism groups
In this paper, it is proved that all simple $K_4$-groups of type $L_2(q)$ can be characterized by their maximum element orders together with their orders. Furthermore, the automorphism groups of simple $K_4$-groups of type $L_2(q)$ are also considered.
متن کاملCompact Metrizable Groups Are Isometry Groups of Compact Metric Spaces
This note is devoted to proving the following result: given a compact metrizable group G, there is a compact metric space K such that G is isomorphic (as a topological group) to the isometry group of K.
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: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.2307/2038611