arXiv subjects

Tomasz Kochanek

Publications and source records attributed to Tomasz Kochanek.

21 records · Page 2Linked to original sources

arXiv2012

$\mathcal F$-bases with brackets and with individual brackets in Banach spaces

We provide a partial answer to the question of Vladimir Kadets whether given an $\mathcal F$-basis of a Banach space $X$, with respect to some filter $\mathcal F\subset \mathcal P(\mathbb N)$, the coordinate functionals are continuous. The answer is positive if the character of $\mathcal F$ is less than $\mathfrak{p}$. In this case every $\mathcal F$-basis with individual brackets is an $M$-basis with brackets determined by a set from $\mathcal F$.

math.FA↗

arXiv2012

Almost orthogonally additive functions

If a function $f$, acting on a Euclidean space $\mathbb{R}^n$, is "almost" orthogonally additive in the sense that $f(x+y)=f(x)+f(y)$ for all $(x,y)\in\bot\setminus Z$, where $Z$ is a "negligible" subset of the $(2n-1)$-dimensional manifold $\bot\subset\mathbb{R}^{2n}$, then $f$ coincides almost everywhere with some orthogonally additive mapping.

math.CA↗

arXiv2012

Characterisation of $L_p$-norms via Hölder's inequality

We characterise $L_p$-norms on the space of integrable step functions, defined on a probabilistic space, via Hölder's type inequality with an optimality condition.

math.FA↗