Journal of Formalized Mathematics
Volume 3, 1991
University of Bialystok
Copyright (c) 1991 Association of Mizar Users

## Introduction to Banach and Hilbert Spaces --- Part I

Jan Popiolek
Warsaw University, Bialystok

### Summary.

Basing on the notion of real linear space (see [11]) we introduce real unitary space. At first, we define the scalar product of two vectors and examine some of its properties. On the base of this notion we introduce the norm and the distance in real unitary space and study properties of these concepts. Next, proceeding from the definition of the sequence in real unitary space and basic operations on sequences we prove several theorems which will be used in our further considerations.

#### MML Identifier: BHSP_1

The terminology and notation used in this paper have been introduced in the following articles [4] [12] [1] [9] [5] [2] [3] [13] [8] [6] [11] [10] [7]

Contents (PDF format)

#### Bibliography

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