APPROXIMATELY MULTIPLICATIVE MAPS FROM WEIGHTED SEMILATTICE ALGEBRAS
APPROXIMATELY MULTIPLICATIVE MAPS FROM WEIGHTED SEMILATTICE ALGEBRAS
复制标题
加权半格代数的近似乘法映射
DOI：
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发表时间：
2012
影响因子：
0.7
通讯作者：
Yemon Choi
中科院分区：
文献类型：
--
作者：
Yemon Choi
Abstract We investigate which weighted convolution algebras ${ ell }_{omega }^{1} (S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson [‘Approximately multiplicative functionals’, J. Lond. Math. Soc. (2) 34(3) (1986), 489–510]. We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, as are all ${ ell }_{omega }^{1} (S)$ where $S$ has either finite width or finite height. Some of these finite-width examples are isomorphic to function algebras studied by Feinstein [‘Strong Ditkin algebras without bounded relative units’, Int. J. Math. Math. Sci. 22(2) (1999), 437–443]. We also investigate when $({ ell }_{omega }^{1} (S), { mathbb{M} }_{2} )$ is an AMNM pair in the sense of Johnson [‘Approximately multiplicative maps between Banach algebras’, J. Lond. Math. Soc. (2) 37(2) (1988), 294–316], where ${ mathbb{M} }_{2} $ denotes the algebra of $2 imes 2$ complex matrices. In particular, we obtain the following two contrasting results: (i) for many nontrivial weights on the totally ordered semilattice ${ mathbb{N} }_{min } $, the pair $({ ell }_{omega }^{1} ({ mathbb{N} }_{min } ), { mathbb{M} }_{2} )$ is not AMNM; (ii) for any semilattice $S$, the pair $({ell }^{1} (S), { mathbb{M} }_{2} )$ is AMNM. The latter result requires a detailed analysis of approximately commuting, approximately idempotent $2 imes 2$ matrices.
Abstract We investigate which weighted convolution algebras ${ ell }_{omega }^{1} (S)$, where $S$ is a semilattice, are AMNM in the sense of Johnson [‘Approximately multiplicative functionals’, J. Lond. Math. Soc. (2) 34(3) (1986), 489–510]. We give an explicit example where this is not the case. We show that the unweighted examples are all AMNM, as are all ${ ell }_{omega }^{1} (S)$ where $S$ has either finite width or finite height. Some of these finite-width examples are isomorphic to function algebras studied by Feinstein [‘Strong Ditkin algebras without bounded relative units’, Int. J. Math. Math. Sci. 22(2) (1999), 437–443]. We also investigate when $({ ell }_{omega }^{1} (S), { mathbb{M} }_{2} )$ is an AMNM pair in the sense of Johnson [‘Approximately multiplicative maps between Banach algebras’, J. Lond. Math. Soc. (2) 37(2) (1988), 294–316], where ${ mathbb{M} }_{2} $ denotes the algebra of $2 imes 2$ complex matrices. In particular, we obtain the following two contrasting results: (i) for many nontrivial weights on the totally ordered semilattice ${ mathbb{N} }_{min } $, the pair $({ ell }_{omega }^{1} ({ mathbb{N} }_{min } ), { mathbb{M} }_{2} )$ is not AMNM; (ii) for any semilattice $S$, the pair $({ell }^{1} (S), { mathbb{M} }_{2} )$ is AMNM. The latter result requires a detailed analysis of approximately commuting, approximately idempotent $2 imes 2$ matrices.
半群代数和 Segal 代数的近似服从性
影响因子：
1.8
作者：
Dales H
通讯作者：
Dales H