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]
-
Preliminaries
-
Summability
-
Necessary and Sufficient Condition for Summability
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Journal of Formalized Mathematics,
15, 2003.
Received February 25, 2003
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