论文标题
Banach的空间，其空间具有$ 2^{\ Mathfrak C} $关闭理想
Banach spaces for which the space of operators has $2^{\mathfrak c}$ closed ideals
论文作者
论文摘要
我们制定了一般条件，这意味着$ l（x，y）$，是从Banach Space $ x $到Banach Space $ Y $的运营商的空间，具有$ 2^{\ Mathfrak C} $封闭的理想，其中$ \ Mathfrak C $是连续性的基础性。这些结果应用于经典序列空间和Tsirelson型空间。特别是，我们证明了$ l（\ ell_p \ oplus \ ell_q）$的一组封闭理想的基数恰好是$ 2^{\ mathfrak c} $，全部$ 1 <p <q <q <q <q <\ infty $又提供了约翰逊和Schechtman $ l _ $ 2^$ 2^$ 2^的最新结果以$ 1 <p \ neq 2 <\ infty $。
We formulate general conditions which imply that $L(X,Y)$, the space of operators from a Banach space $X$ to a Banach space $Y$, has $2^{\mathfrak c}$ closed ideals where $\mathfrak c$ is the cardinality of the continuum. These results are applied to classical sequence spaces and Tsirelson type spaces. In particular, we prove that the cardinality of the set of closed ideals in $L(\ell_p\oplus\ell_q)$ is exactly $2^{\mathfrak c}$ for all $1<p<q<\infty$, which in turn gives an alternate proof of the recent result of Johnson and Schechtman that $L(L_p)$ also has $2^{\mathfrak c}$ closed ideals for $1<p\neq 2<\infty$.
