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2008/2009 Spaces Of p-Tensor Integrable Functions and Related Banach Space Properties
Santwana Basu, N. D. Chakraborty
Real Anal. Exchange 34(1): 87-104 (2008/2009).


In [9] G. F. Stefansson has studied the Banach space $L_1(\nu, X, Y)$, the space of all tensor integrable functions $f : \Omega \to X $ with respect to a countably additive vector valued measure $\nu : \to \Sigma \to Y$ and also the tensor integral of weakly $\nu$-measurable functions. In [1] we obtained some Banach space properties of $L_1(\nu, X, Y)$ and also of w-$L_1(\nu, X, Y)$, the space of all weakly tensor integrable functions. In the present paper, for $1 < p < \infty$, we define the spaces $L_p(\nu, X, Y)$ and w-$L_p(\nu, X, Y)$ of all $\check \otimes_p$-integrable functions and weakly $\check \otimes_p$-integrable functions respectively and discuss several basic properties of these spaces. We also study vector measure duality in $L_p(\nu, X, Y)$ for $1 < p < \infty$.


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Santwana Basu. N. D. Chakraborty. "Spaces Of p-Tensor Integrable Functions and Related Banach Space Properties." Real Anal. Exchange 34 (1) 87 - 104, 2008/2009.


Published: 2008/2009
First available in Project Euclid: 19 May 2009

MathSciNet: MR2527124

Primary: 28B05 , 46G10
Secondary: 46B99

Keywords: Banach space , tensor integrable , vector measure duality

Rights: Copyright © 2008 Michigan State University Press

Vol.34 • No. 1 • 2008/2009
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