2023/01/31 by Abderrahim Baghdad, Baghdad, Abderrahim, El Hassan Benabdi +3
Computer Science · Mathematics · #46C05 #47A10 #47A12 #47B20 #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2302.00550
openalex publication_date 2023/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper considers some new properties of the so-called A-maximal numerical range of operators, denoted by WmaxA(⋅), where A is a positive bounded linear operator acting on a complex Hilbert space H. Some characterizations of A-normaloid operators are also given. In particular, we extend a recent recent by Spitkovsky in [Oper. Matrices, 13, 3(2019)]. Namely, it is shown that an A-bounded linear operator T acting on H is A-normaloid if and only if WmaxA(T)∩ ∂ WA(T)≠\varnothing. Here ∂ WA(T) stands for the boundary of A-numerical range of T. Some new A-numerical radius inequalities generalizing and improving earlier well-known results are also given.