Related papers: Decompositions of matrices by using commutators

We investigate properties of Waring decompositions of real homogeneous forms. We study the moduli of real decompositions, so-called Space of Sums of Powers, naturally included in the Variety of Sums of Powers. Explicit results are obtained…

We prove several versions of Grothendieck's Theorem for completely bounded linear maps $T\colon E \to F^*$, when E and F are operator spaces. We prove that if E,F are $C^*$-algebras, of which at least one is exact, then every completely…

Inspired by some problems in Quantum Information Theory, we present some results concerning decompositions of positive operators acting on finite dimensional Hilbert spaces. We focus on decompositions by families having geometrical symmetry…

A $7$-tuple of commuting bounded operators $\mathbf{T} = (T_1, \dots, T_7)$ defined on a Hilbert space $\mathcal{H}$ is said to be a \textit{$\Gamma_{E(3; 3; 1, 1, 1)}$-contraction} if $\Gamma_{E(3; 3; 1, 1, 1)}$ is a spectral set for…

In the given article infinite order decompositions of C$^*$-algebras are investigated. We give complete proofs of the following statements: 1) If the order unit space $\sum_{\xi,\eta}^\oplus p_\xi Ap_\eta$ is monotone complete in $B(H)$…

Let End(V) denote the ring of all linear transformations of an arbitrary k-vector space V over a field k. We define a subset X of End(V) to be "triangularizable" if V has a well-ordered basis such that X sends each vector in that basis to…

We present a Hilbert space approach to the limit joint *-distributions of complex independent Gaussian random matrices. For that purpose, we use a suitably defined family of creation and annihilation operators living in some direct integral…

By making use of some techniques based upon certain inverse new pairs of symbolic operators, the author investigate several decomposition formulas associated with Humbert hypergeometric functions $\Phi_1 $, $\Phi_2 $, $\Phi_3 $, $\Psi_1 $,…

We obtain the decomposition of the tensor space $\mathfrak{sl}_n^{\otimes k}$ as a module for $\mathfrak{sl}_n$, find an explicit formula for the multiplicities of its irreducible summands, and (when $n \ge 2k$) describe the centralizer…

We study a nonlinear analogue of additive commutators, known as \textit{polynomial commutators}, defined by $p(ab) - p(ba)$ for a polynomial $p \in F[x]$ and elements $a, b$ in an algebra $R$ over a field $F$. Originally introduced by…

Braman [B08] described a construction where third-order tensors are exactly the set of linear transformations acting on the set of matrices with vectors as scalars. This extends the familiar notion that matrices form the set of all linear…

Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…

We study indecomposable representations of quivers on separable infinite-dimensional Hilbert spaces by bounded operators. We consider a complement of Gabriel's theorem for these representations. Let $\Gamma$ be a finite, connected quiver.…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

We generalize the formulation of non-commutative quantum mechanics to three dimensional non-commutative space. Particular attention is paid to the identification of the quantum Hilbert space in which the physical states of the system are to…

Let $D$ be a commutative domain with field of fractions $K$, let $A$ be a torsion-free $D$-algebra, and let $B$ be the extension of $A$ to a $K$-algebra. The set of integer-valued polynomials on $A$ is ${\rm Int}(A) = \{f \in B[X] \mid f(A)…

We prove that if an orientable 3-manifold $M$ admits a complete Riemannian metric whose scalar curvature is positive and has a subquadratic decay at infinity, then it decomposes as a (possibly infinite) connected sum of spherical manifolds…

We study the symmetric tensor rank of multiplication over finite field extensions using linearized polynomials. Via field trace, symmetric linearized polynomials are identified with symmetric bilinear forms and symmetric matrices, allowing…

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Let T be a bounded operator on a Hilbert space H, and F = {f_j: j in J} an at most countable set of vectors in H. In this note, we characterize the pairs {T, F} such that {T^n f: f in F, n in I} form a frame of H, for the cases of I = N_0…