Introduction to Banach and Hilbert Spaces — Part III
Introduction to Banach and Hilbert Spaces — Part III
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巴拿赫空间和希尔伯特空间简介 - 第三部分
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发表时间：
1991
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通讯作者：
J. Popiołek
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作者：
J. Popiołek
第[9]、[2]、[10]、[1]、[12]、[3]、[4]、[5]、[11]、[6]、[7]和[8]条为本文提供了符号和术语。为简便起见，我们采用如下约定：X是一个真实的酉空间，x g是X上的点，a，r，M是真实的数，s1，s2，s3，s4是X上的序列，N1是自然数的递增序列，k，n是自然数。让我们考虑X，让我们考虑s1。我们说s_1是柯西的当且仅当：（定义1）对任意r，使得r> 0，存在sk，使得对所有n，m，使得n ≥ k且m ≥ k保持ρ（s_1（n），s_1（m））< r。我们引入了s1是Cauchy列作为s1是Cauchy列的同义词。以下命题是正确的：
The articles [9], [2], [10], [1], [12], [3], [4], [5], [11], [6], [7], and [8] provide the notation and terminology for this paper. For simplicity, we adopt the following convention: X is a real unitary space, x g are points ofX, a, r, M are real numbers, s1, s2, s3, s4 are sequences of X, N1 is an increasing sequence of naturals, andk, n, mare natural numbers. Let us consider X and let us consider s1. We say that s1 is Cauchy if and only if: (Def. 1) For everyr such thatr > 0 there existsk such that for alln, m such thatn≥ k andm≥ k holdsρ(s1(n),s1(m)) < r. We introduces1 is a Cauchy sequence as a synonym of s1 is Cauchy. The following propositions are true: