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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.

### Article Information

 Title The integration of operator-valued functions with respect to vector-valued measures Source Methods Funct. Anal. Topology, Vol. 18 (2012), no. 3, 288-304 MathSciNet MR3051797 zbMATH 1265.60100 Copyright The 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

### 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},
}