巴拿赫空间中绝对收敛的well-ordered级数的重排
Rearranging absolutely convergent well-ordered series in Banach spaces
摘要：
重新排列级数的项是一种有用的数学方法，而且我们知道什么时候可以这样做而不影响级数的收敛性或总和。例如，如果一系列实数绝对收敛，我们可以分别将偶数索引项和奇数索引项相加，或者将这些项排列在一个无限二维表中，先计算每列的和。更复杂的重新排序的可能性促使我们找到一个普遍的基本原则。我们在巴拿赫空间中证明了这样一个原理，在这里我们考虑指数超过ω但严格低于ω_1的良序级数。证明了对每一个以可数序数为指标的绝对收敛良序级数，若按任一可数序数重排该级数，则该级数的绝对收敛性及和保持不变.
英文摘要：
Reordering the terms of a series is a useful mathematical device, and much is known about when it can be done without affecting the convergence or the sum of the series. For example, if a series of real numbers absolutely converges, we can add the even-indexed and odd-indexed terms separately, or arrange the terms in an infinite two-dimensional table and first compute the sum of each column. The possibility of even more intricate re-orderings prompts us to find a general underlying principle. We identify such a principle in the setting of Banach spaces, where we consider well-ordered series with indices beyond ω, but strictly under ω_1 . We prove that for every absolutely convergent well-ordered series indexed by a countable ordinal, if the series is rearranged according to any countable ordinal, then the absolute convergence and the sum of the series remain unchanged.
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