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The integration of operator-valued functions with respect to vector-valued measures


Abstract

We investigate the $H$-stochastic integral introduced in [24]. It is known that this integral generalizes the classical Ito stochastic integral and the Ito integral on a Fock space. In the present paper we construct and study an extension of the $H$-stochastic integral which will generalize the Hitsuda-Skorokhod integral.

Key words: Hitsuda-Skorohod integral, resolution of identity, Fock space.


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Article Information

TitleThe integration of operator-valued functions with respect to vector-valued measures
SourceMethods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 288-304
MathSciNet MR3051797
zbMATH 1265.60100
CopyrightThe Author(s) 2012 (CC BY-SA)

Authors Information

Volodymyr Tesko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 


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Citation Example

Volodymyr Tesko, The integration of operator-valued functions with respect to vector-valued measures, Methods Funct. Anal. Topology 18 (2012), no. 3, 288-304.


BibTex

@article {MFAT654,
    AUTHOR = {Tesko, Volodymyr},
     TITLE = {The integration of operator-valued functions with respect to vector-valued measures},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {18},
      YEAR = {2012},
    NUMBER = {3},
     PAGES = {288-304},
      ISSN = {1029-3531},
  MRNUMBER = {MR3051797},
 ZBLNUMBER = {1265.60100},
       URL = {http://mfat.imath.kiev.ua/article/?id=654},
}


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