A two-sided sequence ${\left(cₙ\right)}_{n\in \mathbb{Z}}$ with values in a complex unital Banach algebra is a cosine sequence if it satisfies $c_{n+m}+c_{n-m}=2cₙcₘ$ for any n,m ∈ ℤ with c₀ equal to the unity of the algebra. A cosine sequence ${\left(cₙ\right)}_{n\in \mathbb{Z}}$ is bounded if $su{p}_{n\in \mathbb{Z}}\left|\right|cₙ\left|\right|<\infty$. A (bounded) group decomposition for a cosine sequence $c={\left(cₙ\right)}_{n\in \mathbb{Z}}$ is a representation of c as $cₙ=(bⁿ+b^{-n})/2$ for every n ∈ ℤ, where b is an invertible element of the algebra (satisfying $su{p}_{n\in \mathbb{Z}}\left|\right|bⁿ\left|\right|<\infty$, respectively). It is known that every bounded cosine sequence possesses a universally defined group decomposition, here referred...

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

A hybrid flexible beam equation with harmonic disturbance at the end where a rigid tip body is attached is considered. A simple motor torque feedback control is designed for which only the measured time-dependent angle of rotation and its velocity are utilized. It is shown that this control can impel the amplitude of the attached rigid tip body tending to zero as time goes to infinity.

It is shown that every almost linear Pexider mappings $f$, $g$, $h$ from a unital $C^{*}$-algebra $𝒜$ into a unital $C^{*}$-algebra $ℬ$ are homomorphisms when $f\left(2^{n}uy\right)=f\left(2^{n}u\right)f\left(y\right)$, $g\left(2^{n}uy\right)=g\left(2^{n}u\right)g\left(y\right)$ and $h\left(2^{n}uy\right)=h\left(2^{n}u\right)h\left(y\right)$ hold for all unitaries $u\in 𝒜$, all $y\in 𝒜$, and all $n\in \mathbb{Z}$, and that every almost linear continuous Pexider mappings $f$, $g$, $h$ from a unital $C^{*}$-algebra $𝒜$ of real rank zero into a unital $C^{*}$-algebra $ℬ$ are homomorphisms when $f\left(2^{n}uy\right)=f\left(2^{n}u\right)f\left(y\right)$, $g\left(2^{n}uy\right)=g\left(2^{n}u\right)g\left(y\right)$ and $h\left(2^{n}uy\right)=h\left(2^{n}u\right)h\left(y\right)$ hold for all $u\in \{v\in 𝒜\mid v=v^{*}\text{and}v\text{is}\text{invertible}\}$, all $y\in 𝒜$ and all $n\in \mathbb{Z}$. Furthermore, we prove the Cauchy-Rassias stability of $*$-homomorphisms between unital $C^{*}$-algebras, and $ℂ$-linear...

Viene dimostrata l'esistenza di soluzioni del problema di Darboux per l'equazione iperbolica $z_{xy}^{\mathrm{\prime \prime }}=f(x,y,z,Z_x^{\prime },z_y)$ sul planiquarto $x\ge 0$, $y\ge 0$. Qui, $f$ è una funzione continua, con valori in uno spazio Banach che soddisfano alcune condizioni di regolarità espresse in termini della misura di non-compattezza $\alpha$.

In this paper the hyponormal operators on Krein spaces are introduced. We state conditions for the hyponormality of bounded operators focusing, in particular, on those operators $T$ for which there exists a fundamental decomposition $𝕂={𝕂}^{+}\oplus {𝕂}^{-}$ of the Krein space $𝕂$ with ${𝕂}^{+}$ and ${𝕂}^{-}$ invariant under $T$.

We use a non-commutative generalization of the Banach Principle to show that the classical individual ergodic theorem for subsequences generated by means of uniform sequences can be extended to the von Neumann algebra setting.