A. Paszkiewicz

activity

20052024

most citedLarge free linear algebras of real and complex functions

20 citations · 36 across the 8 of their papers we have counts for

collaborators

10 papers

math.MG2024

The Convex Peano Curve Does Exist

Adam Paszkiewicz

We refer here to the surprising construction made by Giuseppe Peano in 1890. He gave an example of a continuous function (called now the Peano curve) from the unit interval to the…

math.FA2015

Strange products of projections

Eva Kopecká, Adam Paszkiewicz

Let $H$ be an infinite dimensional Hilbert space. We show that there exist three orthogonal projections $X_{1}, X_{2}, X_{3}$ onto closed subspaces of $H$ such that for every $0\ne z_0\i…

math.FA2014

Sums of compositions of pairs of projections

Andrzej Komisarski, Adam Paszkiewicz

We give some necessary and sufficient conditions for the possibility to represent a Hermitian operator on an infinite-dimensional Hilbert space (real or complex) in the form $\sum_…

math.FA2014

On the stability of the existence of fixed points for the projection-iterative methods with relaxation

Andrzej Komisarski, Adam Paszkiewicz

We consider an $α$ -relaxed projection $P_{A}^{α} : H \to H$ given by $P_{A}^{α} (x) = α P_{A} (x) + (1 - α) x$ where $α \in [0, 1]$ and $P_{A}$ is the projection onto a non-empty, convex and closed subset $A$ …

math.RA2012★ 20 cited

Large free linear algebras of real and complex functions

Artur Bartoszewicz, Szymon Gł\cab, Adam Paszkiewicz

Let $X$ be a set of cardinality $κ$ such that $κ^{ω} = κ$ . We prove that the linear algebra $R^{X}$ (or $C^{X}$ ) contains a free linear algebra with $2^{κ}$ generators. Usi…

math.FA2012★ 1 cited

In the Amemiya-Ando problem 3 is enough

Adam Paszkiewicz

In any infinite dimensional Hilbert space $H$ there exist orthogonal projections $Q_{1}$ , $Q_{2}$ and $Q_{3}$ , such that a sequence $(P_{n} ... P_{1} (x))$ diverges in norm for some $…