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 .

#### MML Identifier: BHSP_6

The terminology and notation used in this paper have been introduced in the following articles                      

#### Contents (PDF format)

1. Preliminaries
2. Summability
3. Necessary and Sufficient Condition for Summability

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