Volume 15, 2003

University of Bialystok

Copyright (c) 2003 Association of Mizar Users

**Noboru Endou**- Gifu National College of Technology
**Yasumasa Suzuki**- Take, Yokosuka-shi, Japan
**Yasunari Shidama**- Shinshu University, Nagano

- A continuation of [17]. As the example of real unitary spaces, we introduce the arithmetic addition and multiplication in the set of square sum able real sequences and introduce the scaler products also. This set has the structure of the Hilbert space.

- Hilbert Space of Real Sequences
- Miscellaneous

- [1]
Grzegorz Bancerek.
The ordinal numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [2]
Czeslaw Bylinski.
Functions and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989. - [3]
Czeslaw Bylinski.
Functions from a set to a set.
*Journal of Formalized Mathematics*, 1, 1989. - [4]
Czeslaw Bylinski.
Some basic properties of sets.
*Journal of Formalized Mathematics*, 1, 1989. - [5]
Noboru Endou, Yasumasa Suzuki, and Yasunari Shidama.
Real linear space of real sequences.
*Journal of Formalized Mathematics*, 15, 2003. - [6]
Krzysztof Hryniewiecki.
Basic properties of real numbers.
*Journal of Formalized Mathematics*, 1, 1989. - [7]
Jaroslaw Kotowicz.
Convergent sequences and the limit of sequences.
*Journal of Formalized Mathematics*, 1, 1989. - [8]
Jaroslaw Kotowicz.
Monotone real sequences. Subsequences.
*Journal of Formalized Mathematics*, 1, 1989. - [9]
Jaroslaw Kotowicz.
Real sequences and basic operations on them.
*Journal of Formalized Mathematics*, 1, 1989. - [10]
Jan Popiolek.
Real normed space.
*Journal of Formalized Mathematics*, 2, 1990. - [11]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part I.
*Journal of Formalized Mathematics*, 3, 1991. - [12]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part II.
*Journal of Formalized Mathematics*, 3, 1991. - [13]
Jan Popiolek.
Introduction to Banach and Hilbert spaces --- part III.
*Journal of Formalized Mathematics*, 3, 1991. - [14]
Konrad Raczkowski and Andrzej Nedzusiak.
Series.
*Journal of Formalized Mathematics*, 3, 1991. - [15]
Andrzej Trybulec.
Tarski Grothendieck set theory.
*Journal of Formalized Mathematics*, Axiomatics, 1989. - [16]
Andrzej Trybulec.
Subsets of real numbers.
*Journal of Formalized Mathematics*, Addenda, 2003. - [17]
Wojciech A. Trybulec.
Vectors in real linear space.
*Journal of Formalized Mathematics*, 1, 1989. - [18]
Zinaida Trybulec.
Properties of subsets.
*Journal of Formalized Mathematics*, 1, 1989. - [19]
Edmund Woronowicz.
Relations and their basic properties.
*Journal of Formalized Mathematics*, 1, 1989.

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