Biflatness and biprojectivity properties of Banach algebras related to a closed ideal
کد مقاله : 1001-SHAA
امیر سهامی *1، محسن رحیم بیگی2، منا عاج3
1دانشگاه ایلام
2دانشگاه فرهنگیان ایلام
3دبیر اموزش پرورش
چکیده مقاله:
In this note, some new notions of Banach homology, like $I$-biflatness and
$I$-biprojectivity, for a Banach algebra $A$ are defined, where $I$ is a closed
ideal of $A$. As an application, we show that $M(G)$ is $L^{1}(G)$-biprojective
($I$-biflat) if and only if $G$ is a compact group (an amenable
group), respectively. Also for a non-zero ideal $I$, we prove that
if the Fourier algebra $A(G)$ is $I$-biprojective, then $G$ is a
discrete group. To show the differences with classical notions we stablish some examples.
کلیدواژه ها:
Amenability, $I$-biflatness, $I$-biprojectivity
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