In this paper we construct and study an integral of operator-valued functions with respect to Hilbert space-valued measures generated by a resolution of identity. Our integral generalizes the Itô stochastic integral with respect to normal martingales and the Itô integral on a Fock space.
@article{CML_2010__2_1_135_0,
author = {Tesko, Volodymyr},
title = {Hilbert space-valued integral of operator-valued functions},
journal = {Confluentes Mathematici},
pages = {135--157},
publisher = {World Scientific Publishing Co Pte Ltd},
volume = {2},
number = {1},
year = {2010},
doi = {10.1142/S1793744210000144},
language = {en},
url = {http://www.numdam.org/articles/10.1142/S1793744210000144/}
}
TY - JOUR AU - Tesko, Volodymyr TI - Hilbert space-valued integral of operator-valued functions JO - Confluentes Mathematici PY - 2010 SP - 135 EP - 157 VL - 2 IS - 1 PB - World Scientific Publishing Co Pte Ltd UR - http://www.numdam.org/articles/10.1142/S1793744210000144/ DO - 10.1142/S1793744210000144 LA - en ID - CML_2010__2_1_135_0 ER -
%0 Journal Article %A Tesko, Volodymyr %T Hilbert space-valued integral of operator-valued functions %J Confluentes Mathematici %D 2010 %P 135-157 %V 2 %N 1 %I World Scientific Publishing Co Pte Ltd %U http://www.numdam.org/articles/10.1142/S1793744210000144/ %R 10.1142/S1793744210000144 %G en %F CML_2010__2_1_135_0
Tesko, Volodymyr. Hilbert space-valued integral of operator-valued functions. Confluentes Mathematici, Tome 2 (2010) no. 1, pp. 135-157. doi : 10.1142/S1793744210000144. http://www.numdam.org/articles/10.1142/S1793744210000144/
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