arXiv subjects
Publications and source records attributed to S. P. Murugan.
A new generalization of Fiedler's lemma is obtained by introducing the concept of the main function of a matrix. As applications, the universal spectra of the H-join, the spectra of the H-generalized join and the spectra of the generalized corona of any graphs (possibly non-regular) are obtained.
Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $Ω$. Let $E$ be a product system over $Ω$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $α:=\{α_x\}_{x \in P}$ of unital normal $*$-endomorphisms of $B(\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $α$.
Let $S \subset \mathbb{Z}^{d}$ be a finitely generated subsemigroup. Let $E$ be a product system over $S$. We show that there exists an infinite dimensional separable Hilbert space $\mathcal{H}$ and a semigroup $α:=\{α_x\}_{x \in S}$ of unital normal $*$-endomorphisms of $B(\mathcal{H})$ such that $E$ is isomorphic to the product system associated to $α$.
Let $P$ be a closed convex cone in $\mathbb{R}^{n}$. Assume that $P$ is spanning i.e. $P-P=\mathbb{R}^{n}$ and pointed i.e. $P \cap -P=\{0\}$. Let $α:=\{α_{x}:x \in P\}$ be a $σ$-weakly continuous family of unital normal endomorphisms on $B(H)$. Denote the "product system" associated to $α$ by $\mathcal{E}_α$. We show that $\mathcal{E}_α$ is a concrete product system and $α$, up to cocycle conjugacy, can be recovered completely from $\mathcal{E}_α$