We consider a complex symmetric sequence space E that possesses the Fatou property and is different from l2. We prove that, for every surjective linear isometry V on E, there exist λn ∈ ℂ with |λn| =

It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\mathcal C_E \not =\mathcal C_{2}$ of compact operators, acting in a complex separable infinite-dimensional Hilbert space $\mathcal H$, there exist unitary ope

The Hitchcock-Koopmans transportation problem is a well-known and fundamental optimization problem which focuses on minimization of the objective function which is basically the transportation cost from multiple sources to multiple destinations. In this article, we present some novel results on the spectral properties of structured matrices appearing in Hitchcock-Koopmanstransportation problems. The results on the computation of singular values are presented with usage of tools from linear algebra and matrix analysis. The new results are derived on interconnection between structured singular values of pseudo-inverse and D-stable matrices of Hitchcock-Koopmans transportation models. The numerical experimentation shows the behavior of singular values. The Matlab EigTool is used for the computation of pseudo-spectrum of pseudo-inverse matrix corresponding to the transportation model.

In this article, we consider simple-motion pursuit–evasion differential games in the Hilbert space of square summable sequences. We show that when the players have the same dynamic capabilities, evasion is possible under some assumptions about the initial positions of the players.

It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\mathcal C_E\neq \mathcal C_2$ of compact operators, acting in a complex separable infnite-dimensional Hilbert space $\mathcal H$ there exist unitary operators $u$ and $v$ on $\mathcal H$ such that $V(x)=uxv$ or $V(x) = ux^tv$ for all $x\in \mathcal C_E$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $\mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $\mathcal C_E \neq \mathcal C_2$ is a linear isometry on $\mathcal C_E$.