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pro vyhledávání: '"47a12"'
This paper presents a study of the generalized Davis-Wielandt radius of Hilbert space operators. New lower bounds for the generalized Davis-Wielandt radius and numerical radius are provided. An alternative of the triangular inequality for operators i
Externí odkaz:
http://arxiv.org/abs/2410.19679
We investigate when the algebraic numerical range is a $C$-spectral set in a Banach algebra. While providing several counterexamples based on classical ideas as well as combinatorial Banach spaces, we discuss positive results for matrix algebras and
Externí odkaz:
http://arxiv.org/abs/2410.10678
Autor:
Bhunia, Pintu
Let $\mathcal{A}$ be a unital $\mathbf{C}^*$-algebra with unit $e$. We develop several inequalities for a positive linear functional $f$ on $\mathcal{A}$ and obtain several bounds for the numerical radius $v(a)$ of an element $a\in \mathcal{A}$. Amon
Externí odkaz:
http://arxiv.org/abs/2410.02435
Autor:
Rashid, M. H. M.
In this paper, we aim to establish a range of numerical radius inequalities. These discoveries will bring us to a recently validated numerical radius inequality and will present numerical radius inequalities that exhibit enhanced precision when compa
Externí odkaz:
http://arxiv.org/abs/2410.03563
Autor:
Schwenninger, F. L., de Vries, J.
We thoroughly analyse the double-layer potential's role in approaches to spectral sets in the spirit of Delyon--Delyon, Crouzeix and Crouzeix--Palencia. While the potential is well-studied, we aim to clarify on several of its aspects in light of thes
Externí odkaz:
http://arxiv.org/abs/2409.15954
The Crouzeix ratio $\psi(A)$ of an $N\times N$ complex matrix $A$ is the supremum of $\|p(A)\|$ taken over all polynomials $p$ such that $|p|\le 1$ on the numerical range of $A$. It is known that $\psi(A)\le 1+\sqrt{2}$, and it is conjectured that $\
Externí odkaz:
http://arxiv.org/abs/2409.14127
Publikováno v:
Linear Algebra and its Applications 703 (2024), 20-26
Let $T$ be a injective bounded linear operator on a complex Hilbert space. We characterize the complex numbers $\lambda,\mu$ for which $(I+\lambda T)(I+\mu T)^{-1}$ is a contraction, the characterization being expressed in terms of the numerical rang
Externí odkaz:
http://arxiv.org/abs/2409.14125
This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator tuples. Furth
Externí odkaz:
http://arxiv.org/abs/2410.03669
Autor:
Li, Chi-Kwong, Wang, Kuo-Zhong
We refine a recent result of Drury concerning the optimal ratio between the norm and numerical radius of a bounded linear operator $T$ with numerical range lying in a sector of a circular disk. In particular, characterization is given to the operator
Externí odkaz:
http://arxiv.org/abs/2409.18135
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