Open Access

Operator-valued integral of vector-function and bases


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.

Full Text

Article Information

TitleOperator-valued integral of vector-function and bases
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 318-328
MathSciNet MR2374833
CopyrightThe Author(s) 2007 (CC BY-SA)

Authors Information

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

Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley

Citation Example

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


@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},
  MRNUMBER = {MR2374833},
       URL = {},

All Issues