Zobrazeno 1 - 10
of 42
pro vyhledávání: '"Singla, Sushil"'
Autor:
Kuzma, Bojan, Singla, Sushil
We classify real or complex finite-dimensional $C^*$-algebras and their underlying fields from the properties of Birkhoff-James orthogonality. Application to strong Birkhoff-James orthogonality preservers is also given.
Comment: Accepted for pub
Comment: Accepted for pub
Externí odkaz:
http://arxiv.org/abs/2411.15273
Autor:
Kuzma, Bojan, Singla, Sushil
The main goal of the article is to prove that if $\mathcal A_1$ and $\mathcal A_2$ are Birkhoff-James isomorphic $C^*$-algebras over the fields $\mathbb F_1$ and $\mathbb F_2$, respectively and if $\mathcal A_1$ finite-dimensional, abelian of dimensi
Externí odkaz:
http://arxiv.org/abs/2411.01684
Let $1 \leq k < n$ be integers. Two $n \times n$ matrices $A$ and $B$ form a parallel pair with respect to the $k$-numerical radius $w_k$ if $w_k(A + \mu B) = w_k(A) + w_k(B)$ for some scalar $\mu$ with $|\mu| = 1$; they form a TEA (triangle equality
Externí odkaz:
http://arxiv.org/abs/2408.16066
Autor:
Kuzma, Bojan, Singla, Sushil
A Banach space characterization of simple real or complex $C^*$-algebras is given which even characterizes the underlying field. As an application, it is shown that if $\mathfrak A_1$ and $\mathfrak A_2$ are Birkhoff-James isomorphic simple $C^*$-alg
Externí odkaz:
http://arxiv.org/abs/2407.21582
For an arbitrary normed space $\mathcal X$ over a field $\mathbb F \in \{ \mathbb R, \mathbb C \}$, we define the directed graph $\Gamma(\mathcal X)$ induced by Birkhoff-James orthogonality on the projective space $\mathbb P(\mathcal X)$, and also it
Externí odkaz:
http://arxiv.org/abs/2402.13416
Two bounded linear operators $A$ and $B$ are parallel with respect to a norm $\|\cdot\|$ if $\|A+\mu B\| = \|A\| + \|B\|$ for some scalar $\mu$ with $|\mu| = 1$. Characterization is obtained for bijective linear maps sending parallel bounded linear o
Externí odkaz:
http://arxiv.org/abs/2309.14357
Marc Rieffel had introduced the notion of the quantum Gromov-Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on $2$-sphere in this distance. One finds app
Externí odkaz:
http://arxiv.org/abs/2211.04321
Autor:
Bukoski, Juliana, Singla, Sushil
Many interesting examples of operator algebras, both self-adjoint and non-self-adjoint, can be constructed from directed graphs. In this survey, we overview the construction of $C^*$-algebras from directed graphs and from two generalizations of graph
Externí odkaz:
http://arxiv.org/abs/2209.01661
Autor:
Grover, Priyanka, Singla, Sushil
For a tuple of operators $\boldsymbol{A}= (A_1, \ldots, A_d)$, $\text{dist}(\boldsymbol{A}, \mathbb C^d \boldsymbol{I})$ is defined as $\min\limits_{\boldsymbol{z} \in \mathbb C^d} \|\boldsymbol{A-zI}\|$ and $\text{var}_x (\boldsymbol{A})$ as $\|\bol
Externí odkaz:
http://arxiv.org/abs/2206.01503
We reconsider the theory of Lagrange interpolation polynomials with multiple interpolation points and apply it to linear algebra. For instance, $A$ be a linear operator satisfying a degree $n$ polynomial equation $P(A)=0$. One can see that the evalua
Externí odkaz:
http://arxiv.org/abs/2203.01822