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pro vyhledávání: '"Nayak, Soumyashant"'
Autor:
Nayak, Soumyashant, Shekhawat, Renu
For $A \in M_m(\mathbb{C})$, Yamamoto's generalization of the spectral radius formula (1967) asserts that $\lim_{n \to \infty} s_j(A^n)^{\frac{1}{n}}$ is equal to the $j^{\textrm{th}}$-largest eigenvalue-modulus of $A$, where $s_j (A^n)$ denotes the
Externí odkaz:
http://arxiv.org/abs/2410.16318
Autor:
Ghosh, Indrajit, Nayak, Soumyashant
Publikováno v:
International Mathematics Research Notices, 2024
In this article, we aim to provide a satisfactory algebraic description of the set of affiliated operators for von Neumann algebras. Let $\mathscr{M}$ be a von Neumann algebra acting on a Hilbert space $\mathcal{H}$, and let $\mathscr{M}_{\text{aff}}
Externí odkaz:
http://arxiv.org/abs/2311.16170
Autor:
Nayak, Soumyashant
Publikováno v:
Linear Algebra and its Applications Volume 679, 15 December 2023, Pages 231-245
For a matrix $T \in M_m(\mathbb{C})$, let $|T| : = \sqrt{T^*T}$. For $A \in M_m(\mathbb{C})$, we show that the matrix sequence $\big\{ |A^n|^{\frac{1}{n}} \big\}_{n \in \mathbb{N}}$ converges in norm to a positive-semidefinite matrix $H$ whose $j^{\t
Externí odkaz:
http://arxiv.org/abs/2303.01252
Let $\mathscr{R}$ be a type $II_1$ von Neumann algebra. We show that every unitary in $\mathscr{R}$ may be decomposed as the product of six symmetries (that is, self-adjoint unitaries) in $\mathscr{R}$, and every unitary in $\mathscr{R}$ with finite
Externí odkaz:
http://arxiv.org/abs/2204.00009
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Autor:
Nayak, Soumyashant
Publikováno v:
Banach J. Math. Anal. 14 (2020), 1055-1079
For a countably decomposable finite von Neumann algebra $\mathscr{R}$, we show that any choice of a faithful normal tracial state on $\mathscr{R}$ engenders the same measure topology on $\mathscr{R}$ in the sense of Nelson (J. Func. Anal., 15 (1974),
Externí odkaz:
http://arxiv.org/abs/1911.01978
Autor:
Nayak, Soumyashant
Publikováno v:
Banach J. Math. Anal. 14, 1055--1079 (2020)
Let $\mathscr{M}$ be a $II_1$ factor acting on the Hilbert space $\mathscr{H}$, and $\mathscr{M}_{\textrm{aff}}$ be the Murray-von Neumann algebra of closed densely-defined operators affiliated with $\mathscr{M}$. Let $\tau$ denote the unique faithfu
Externí odkaz:
http://arxiv.org/abs/1812.06872
Autor:
Nayak, Soumyashant
Publikováno v:
Bull. Lond. Math. Soc. 50 (2018), no. 6, 1102--1112
Let $\mathscr{M}$ be a finite von Neumann algebra with a faithful normal tracial state $\tau$ and $\mathfrak{A}$ be a finite subdiagonal subalgebra of $\mathscr{M}$ with respect to a $\tau$-preserving faithful normal conditional expectation $\Phi$ on
Externí odkaz:
http://arxiv.org/abs/1807.11652
Autor:
Nayak, Soumyashant
By a result of Lundquist-Barrett, it follows that the rank of a positive semi-definite matrix is less than or equal to the sum of the ranks of its principal diagonal submatrices when written in block form. In this article, we take a general operator
Externí odkaz:
http://arxiv.org/abs/1804.09683
Autor:
Nayak, Soumyashant
Publikováno v:
J. Operator Theory 89, Issue 2 (Spring 2023), 477--520
For every square matrix $A$ over a field $\mathbb{K}$, we have the equality $\mathrm{rank}(A) + \mathrm{rank}(I-A) = \mathrm{rank}(I) + \mathrm{rank}(A-A^2)$ where $I$ denotes the identity matrix with the same dimensions as $A$. In this article, we s
Externí odkaz:
http://arxiv.org/abs/1801.08072