arXiv subjects

Hana Bendová

Publications and source records attributed to Hana Bendová.

3 recordsLinked to original sources

arXiv2014

Quantification of the Banach-Saks property

We investigate possible quantifications of the Banach-Saks property and the weak Banach-Saks property. We prove quantitative versions of relationships of the Banach-Saks property of a set with norm compactness and weak compactness. We further establish a quantitative version of the characterization of the weak Banach-Saks property of a set using uniform weak convergence and $\ell_1$-spreading models. We also study the case of the unit ball and in this case we prove a dichotomy which is an analogue of the James distortion theorem for $\ell_1$-spreading models.

math.FA↗

arXiv2013

Quantitative Grothendieck Property

A Banach space $X$ is Grothendieck if the weak and the weak$^*$ convergence of sequences in the dual space $X^*$ coincide. The space $\ell^\infty$ is a classical example of a Grothendieck space due to Grothendieck. We introduce a quantitative version of the Grothendieck property, we prove a quantitative version of the above-mentioned Grothendieck's result and we construct a Grothendieck space which is not quantitatively Grothendieck. We also establish the quantitative Grothendieck property of $L^\infty(μ)$ for a $σ$-finite measure $μ$.

math.FA↗

arXiv2010

An elementary way to introduce a Perron-like integral

We give an alternative definition of integral at the generality of the Perron integral and propose an exposition of the foundations of integral theory starting from this new definition. Both definition and proofs needed for the development are unexpectedly simple. We show how to adapt the definition to cover the multidimensional and Stieltjes case and prove that our integral is equivalent to the Henstock-Kurzweil(-Stieltjes) integral.

math.CA↗