Some operator inequalities for unitarily invariant norms [PDF]
, 2023 Let L(H) be the algebra of bounded operators on a complex separable Hilbert space H. Let N be a unitarily invariant norm defined on a norm ideal J ⊆ L(H). Given two positive invertible operators P,Q ∊ L(H) and k ∊ (−2, 2], we show that N (PTQ−1 + P−1TQ +
Mosconi, Irene +2 more
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On quantum ergodicity for higher‐dimensional cat maps modulo prime powers
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract A discrete model of quantum ergodicity of linear maps generated by symplectic matrices A∈Sp(2d,Z)$A \in \operatorname{Sp}(2d,{\mathbb {Z}})$ modulo an integer N⩾1$N\geqslant 1$, has been studied for d=1$d=1$ and almost all N$N$ by Kurlberg and Rudnick (2001, Comm. Math. Phys., 222, 201–227).
Subham Bhakta, Igor E. Shparlinski
wiley +1 more source
Scattering theory for difference equations with operator coefficients
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We investigate a class of second‐order difference equations featuring operator‐valued coefficients with the aim of approaching problems of stationary scattering theory. We focus on various compact perturbations of the discrete Laplacian given in a Hilbert space of bi‐infinite square‐summable sequences with entries from a fixed Hilbert space ...
David Sher +3 more
wiley +1 more source
New perturbation bounds in unitarily invariant norms for subunitary polar factors
, 2018 Let $A\in\mathbb{C}^{m \times n}$ have generalized polar decomposition $A = QH$ with $Q$ subunitary and $H$ positive semidefinite. Absolute and relative perturbation bounds are derived for the subunitary polar factor $Q$ in unitarily invariant norms and ...
Liu, Hao +3 more
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Unitarily invariant valuations on convex functions, I
, 2021 We study continuous, dually epi-translation invariant valuations on ℂⁿ that are invariant under the unitary group and we give a description of all valuations belonging to the dense subspace of smooth valuations.
Knörr, Jonas
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Unitarily invariant norms and tensor products of maximal injective von Neumann subalgebras [PDF]
, 2008 This dissertation consists of four contributions to the study of von Neumann algebras. In the first part, we set up a representation theorem for unitarily invariant norms on finite factor von Neumann algebras.
Fang, Junsheng
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Residual bounds for unitarily invariant norms on clustered eigenvalues [PDF]
, 1997 Let n × n Hermitian matrix A have eigenvalues λ1, λ2, …, λn, let k × k Hermitian matrix H have eigenvalues μ1, μ2, …, μk, and let Q be an n × k matrix having full column rank, so 1 ≤ k ≤ n. It is proved that there exist k eigenvalues λi1 ≤ λi2 … ≤ λik of
Xie, Jian-Jun, Jian-Jun Xie
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Interpolated inequalities for unitarily invariant norms
Linear Algebra and its Applications, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +2 more sources
On the unitarily invariant norms of the matrices connected to complex number sequences [PDF]
, 2020 In this study, we compute the unitarily invariant norms of the matrices A(z) = (z(i)z(j))(i,j=1)(n), B-z = (z(i) - z(j))(i,j=1)(n) and C-z = (z(i)/z(j))(i,j=1)(n), where z(i)s are ith components of any complex sequence (z(n)).
Bahşi, Mustafa
core
Inequalities involving unitarily invariant norms and operator monotone functions [PDF]
, 2002 Let ∥·∥ be a unitarily invariant norm on matrices. For matrices A,B,X with A,B positive semidefinite and X arbitrary, we prove that the function t↦∥|AtXB1−t|r∥·∥|A1−tXBt|r∥ is convex on [0,1] for each r>0.
Hiai, FM +5 more
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