Open Access

# Operator-valued integral of vector-function and bases

### Abstract

In the present paper we are going to introduce an operator-valued integral of a square modulus weakly integrable mappings the ranges of which are Hilbert spaces, as bounded operators. Then, we shall show that each operator-valued integrable mapping of the index set of an orthonormal basis of a Hilbert space $H$ into $H$ can be written as a multiple of a sum of three orthonormal bases.

### Article Information

 Title Operator-valued integral of vector-function and bases Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 318-328 MathSciNet MR2374833 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

M. H. Faroughi
Department of Mathematics, University of Tabriz, Tabriz, Iran

### Citation Example

M. H. Faroughi, Operator-valued integral of vector-function and bases, Methods Funct. Anal. Topology 13 (2007), no. 4, 318-328.

### BibTex

@article {MFAT407,
AUTHOR = {Faroughi, M. H.},
TITLE = {Operator-valued integral of vector-function and bases},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {4},
PAGES = {318-328},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=407},
}