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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.

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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)

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

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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 = {},

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