arXiv subjects

Chandal Nahak

Publications and source records attributed to Chandal Nahak.

4 recordsLinked to original sources

arXiv2026

New perspectives on operator radius bounds in $A-$weighted frameworks

By employing the Moore$-$Penrose inverse of a bounded linear operator, we derive several bounds for the numerical radius and operator norms of the sum of operators in semi$-$Hilbertian space that generalize and improve the classical bounds. We establish novel inequalities pertaining to the $\mathbb{A}$$-$Davis$-$Wielandt radius for $n \times n$ operator matrices and further explore their ramifications, particularly concerning $\mathbb{A}$$-$Davis$-$Wielandt radius bounds for $2 \times 2$ operator matrices, where diagonal operator matrix $\mathbb{A}$ contains positive bounded operator $A.$ Ultimately, we get an improved upper bound for the $A$$-$numerical radius inequalities relating to the commutators of operators.

math.FA↗

arXiv2026

Operator Inequalities and Several Characterizations of the $λ$-Mean Transform

We broaden Buzano-type inequalities to provide novel numerical radius bounds for operators of the type $AXB$, thereby generalizing the results obtained by Sababheh et al. For the $λ$-mean transform $M_λ(T)$, we provide a counterexample demonstrating that $r_σ(M_λ(T)) \le r_σ(T)$ fails to hold in general for $λ\in (0, 1)$, establish that $(r_ω(M_λ(T)))^n$ and $r_ω(T^n)$ are typically incomparable for $n \ge 2$, and confirm that $M_λ(T^*) = (M_λ(T))^*$ is valid for $λ\in [0, 1)$ if and only if $T$ is a member of a newly established $σ$-class. Furthermore, we examine the transformation characteristics of $T$ and the tensor products $T \otimes S$, refine Zamani's inequalities, and unify operator modulus bounds $|\widetilde{T}| \le |\widehat{T}| \le |T|$. In this application, we demonstrate that the conditions for norm preservation, $\|\widetilde{T}\| = \|T\|$ and $\|M_λ(T)\| = \|T\|$, are equivalent to the statement $\|T^2\| = \|T\|^2$, and we offer precise norm estimates for $2 \times 2$ off-diagonal block operator matrices under $λ$-mean transformation.

math.FA↗

arXiv2026

Coloring discrete pseudomanifolds

This paper presents three main results on coloring discrete $d$-pseudomanifolds: $(1)$ the general chromatic bounds $d+1 \leq X(K) \leq 2d+2$ for any $d$-pseudomanifold $K$; $(2)$ an improved bound $X(K) \leq 2d+1$ for pseudomanifolds expressible as a Zykov join $K = S^k + K'$; $(3)$ the optimal bound $X(K)\leq\lceil 3(d+1)/2\rceil$ under the additional assumptions that the spherical join factor $S^k$ is built from even-cycles and its dimension $k$ is close to $d$.

math.CO↗

arXiv2026

Rational stable homotopy type of equivariant projective spaces and Grassmannians

We prove explicit rational stable splittings of equivariant complex projective spaces $\mathbb{C}P(V)$ and Grassmannians $Gr_n(V)$, for complex representations $V$. When $V$ is a sum of one-dimensional representations, both $\mathbb{C}P(V)$ and $Gr_n(V)$ are rationally a wedge of representation spheres. For general finite groups $G$ and $V$ a sum of irreducible representations which are not necessarily one-dimensional, we show that $\mathbb{C}P(V)$ splits rationally as a wedge of Thom spaces over irreducible factors in $V$. For $Gr_n(V)$, the factors in the corresponding rational splitting are a smash product of Thom spaces over lower Grassmannians on irreducible factors in $V$.

math.AT↗