论文标题
Fréchet和（lb）序列空间由离散cesàro空间的双巴拉克空间引起
Fréchet and (LB) sequence spaces induced by dual Banach spaces of discrete Cesàro spaces
论文作者
论文摘要
fréchet（res. \（lb））序列空间$ ces（p+）：= \ cap_ {r> p} ces（r），1 \ leq p <\ infty $（ress.cees（p-）：= \ cup_ {1 <p} ces（r） $ \ ell_ {p+} $（resp。，$ \ ell_ {p _ { - }}）。$这两个类别的不可验证的空间$ ces（p+），ces（p-）$均通过反射式banach序列空间$ ces（p），1 <p <p <p <p <p <p <d $ diul q diul q diul q diul q diul qual q diul q diul q diul q diul q diul q diul q diul q diul q diul q diul q diul q。 G. \ Bennett，A。\ Jagers等人研究了离散的cesàrospaces $ ces（p），1 <p <\ infty。我们的目的是详细研究相应的序列空间$ d（p+）$和$ d（p-），$，以前尚未考虑过。他们的某些属性与$ CES（P+），CES（P-）$具有相似之处，但它们也表现出差异。例如，$ ces（p+）$是订单1的功率系列空间的同构，而$ d（p+）$对这种无限订单的空间是同构的。每个空间$ ces（p+），ces（p-）$都符合绝对基础，但是，没有一个空间$ d（p+），d（p-）$具有绝对的基础。
The Fréchet (resp.\ (LB)) sequence spaces $ces(p+) := \cap_{r > p} ces(r), 1 \leq p < \infty $ (resp.\ $ ces (p-) := \cup_{ 1 < r < p} ces (r), 1 < p \leq \infty),$ are known to be very different to the classical sequence spaces $ \ell_ {p+} $ (resp., $ \ell_{p_{-}}).$ Both of these classes of non-normable spaces $ ces (p+), ces (p-)$ are defined via the family of reflexive Banach sequence spaces $ ces (p), 1 < p < \infty .$ The dual Banach spaces $ d (q), 1 < q < \infty ,$ of the discrete Cesàro spaces $ ces (p), 1 < p < \infty,$ were studied by G.\ Bennett, A.\ Jagers and others. Our aim is to investigate in detail the corresponding sequence spaces $ d (p+) $ and $ d (p-),$ which have not been considered before. Some of their properties have similarities with those of $ ces (p+), ces (p-)$ but, they also exhibit differences. For instance, $ ces (p+)$ is isomorphic to a power series Fréchet space of order 1, whereas $ d (p+) $ is isomorphic to such a space of infinite order. Every space $ ces (p+), ces (p-) $ admits an absolute basis but, none of the spaces $ d (p+), d (p-)$ have any absolute basis.
