Consider a unital $C^*$-algebra $\mathcal{A}$. Let $n\geq 2$ and let $P_1, \ldots , P_n$ be projections in $\mathcal{A}$ such that $P_1 + \ldots +P_n=I$. We costruct $\mathcal{P}_n\colon \mathcal{A}\to \mathcal{A}$ ...

Let $\mathcal{H}$ be a Hilbert space, $\dim \mathcal{H}= +\infty$. Let $X=U|X|$ be the polar decomposition of an operator $X\in \mathcal{B}(\mathcal{H})$. Then $X$ is a non-commutator if and only if both $U$ and ...

We establish similarity between some tripotents and idempotents on a Hilbert space $H$ and obtain new results on differences and commutators of idempotents $P$ and $Q$. In the unital case, the difference $P - Q$ is associated ...

In this paper we give an overview of the evolution of homogeneous and isotropic subspaces in modified multidimensional gravity.

The article describes methodological approaches to the formation of olympiad competencies for juniors, children 12-15 years old, based on five training tracks in olympiad informatics in accordance with the IOI Syllabus. ...

We discuss the way of solving the hierarchy problem. We show that starting at the Planck scale, the three energy scales - inflationary, electroweak and the cosmological ones can be restored. A mechanism for generating small ...

The aim of the present paper is the clarification of the result of A.Paliathanasis, K.Krishnakumar, K.M.Tamizhmani and P.G.L.Leach on the symmetry Lie algebra of the Black-Scholes-Merton equation for European options.

Given a von Neumann algebra $M$ of operators on a Hilbert space $H$ and a faithful normal semifinite trace $\tau$ on $M$, denote by $S(M, \tau)$ the *-algebra of $\tau$-measurable operators. We obtain a sufficient condition ...