Big data storage and processing are considered as one of the main applications for cloud
computing systems. Furthermore, the development of the Internet of Things (IoT) paradigm …

The Cauchy dual subnormality problem asks whether the Cauchy dual operator T′:= T (T⁎
T)− 1 of a 2-isometry T is subnormal. In the present paper we show that the problem has a …

We present some 2-isometric lifting and extension results for Hilbert space concave
operators. For a special class of concave operators we study their Cauchy dual operators …

A study of 3-isometries on a Hilbert space H which have 3-Brownian unitary extensions is
developed. It was inspired by the similar results of Agler-Stankus in the context of 2 …

A bounded linear Hilbert space operator $ S $ is said to be a $2 $-isometry if the operator $
S $ and its adjoint $ S^* $ satisfy the relation $ S^{* 2} S^{2}-2 S^{*} S+ I= 0$. In this paper …

In this paper, we introduce operators that are represented by upper triangular 2 * 2 2× 2
block matrices whose entries satisfy some algebraic constraints. We call them Brownian …

We investigate the operators T on a Hilbert space HH which have 2-isometric liftings S on K
⊃ HK⊃ H such that HH is an invariant subspace for S^* SS∗ S. We describe such operators …

We characterize the unitary equivalence of 2-isometric operators satisfying the so-called
kernel condition. This relies on a model for such operators built on operator-valued …

The B-operators (abbreviation for Brownian-type operators) are upper triangular $2\times 2$
block matrix operators that satisfy certain algebraic constraints. The purpose of this paper is …

We obtain some reducing (or just invariant) subspaces for a Hilbert space operator on which
it acts as a Brownian type 2-isometry. More exactly Brownian isometric (unitary) parts as well …