On Some Properties of Real Hilbert Space. Part I

Journal of Formalized Mathematics
Volume 15, 2003
University of Bialystok
Copyright (c) 2003 Association of Mizar Users

On Some Properties of Real Hilbert Space. Part I

Hiroshi Yamazaki: Shinshu University, Nagano
Yasumasa Suzuki: Take, Yokosuka-shi, Japan
Takao Inoue: The Iida Technical High School, Nagano
Yasunari Shidama: Shinshu University, Nagano

Summary.

In this paper, we first introduce the notion of summability of an infinite set of vectors of real Hilbert space, without using index sets. Further we introduce the notion of weak summability, which is weaker than that of summability. Then, several statements for summable sets and weakly summable ones are proved. In the last part of the paper, we give a necessary and sufficient condition for summability of an infinite set of vectors of real Hilbert space as our main theorem. The last theorem is due to [8].

MML Identifier: BHSP_6

The terminology and notation used in this paper have been introduced in the following articles [17] [21] [6] [1] [18] [9] [22] [4] [5] [7] [12] [19] [14] [15] [13] [3] [10] [16] [11] [2] [20] [23]

Contents (PDF format)

Preliminaries
Summability
Necessary and Sufficient Condition for Summability

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Received February 25, 2003

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