arXiv subjects

Marek Słociński

Publications and source records attributed to Marek Słociński.

4 recordsLinked to original sources

arXiv2024

An operator theory approach to the evanescent part of a two-parametric weak-stationary stochastic process

A new approach to the evanescent part of a two-dimensional weak-stationary stochastic process with the past given by a half-plane is proceed. The classical result due to Helson and Lowdenslager divides a two-parametric weak-stationary stochastic process into three parts. In this paper we describe the most untouchable one - the evanescent part. Moreover, we point out how this part depends on the shape of the past.

math.PR↗

arXiv2019

The decomposition theorems in Baer $*$-rings

We show a general decomposition theorem in Baer *-rings. As a consequence the vast majority of decompositions known in the algebra of bounded Hilbert space operators are generalized to Baer *-rings. There are also results which are new in the algebra of bounded Hilbert space operators. The model of summands in Wold-Słociński decomposition in Baer *-rings is given.

math.RA↗

arXiv2017

Invariant subspaces of $\mathcal{H}^2(\mathbb{T}^2)$ and $L^2(\mathbb{T}^2)$ preserving compatibility

Operators of multiplication by independent variables on the space of square summable functions over the torus and its Hardy subspace are considered. Invariant subspaces where the operators are compatible are described.

math.FA↗

arXiv2012

On the unitary part of isometries in commuting, completely non doubly commuting pairs

There are considered isometries on a Hilbert space. By the Wold theorem any isometry can be decomposed into a unitary operator and a unilateral shift. For a pair of isometries, even commuting, a maximal subspace reducing one isometry to a unitary operator might not reduce the other isometry. In the paper are considered pairs of commuting isometries which are completely non doubly commuting. For such pairs there are no nontrivial subspaces reducing both isometries and one of them to a unitary operator. The results describe a unitary part of an isometry in such a pair.

math.FA↗