Real Analysis Exchange
- Real Anal. Exchange
- Volume 34, Number 1 (2008), 87-104.
Spaces Of p-Tensor Integrable Functions and Related Banach Space Properties
In  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  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 $1 < p < \infty$.
Real Anal. Exchange, Volume 34, Number 1 (2008), 87-104.
First available in Project Euclid: 19 May 2009
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Primary: 46G10: Vector-valued measures and integration [See also 28Bxx, 46B22] 28B05: Vector-valued set functions, measures and integrals [See also 46G10]
Secondary: 46B99: None of the above, but in this section
Chakraborty, N. D.; Basu, Santwana. Spaces Of p -Tensor Integrable Functions and Related Banach Space Properties. Real Anal. Exchange 34 (2008), no. 1, 87--104. https://projecteuclid.org/euclid.rae/1242738922