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Clear All  # О некоторых свойствах пространства тенэорно интегрируемых функций

Authors: N. Chakraborty and Santwana Basu

## Abstract

The tensor integral of a vector valued function f: Ω → X with respect to a countably additive vector valued measure v: Σ → Y has been defined by Stefansson in  and he has investigated many of its properties. The integral is an element of the injective tensor product X

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\smile}}}{ \otimes }$$ \end{document}
Y. We study the Banach space L1(v, X, Y) of all
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\smile}}}{ \otimes }$$ \end{document}
-integrable functions and discuss many properties of this space. We also study the space w-L1(v, X, Y) of all weakly
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\overset{\lower0.5em\hbox{\smash{\scriptscriptstyle\smile}}}{ \otimes }$$ \end{document}
-integrable functions.

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