The weighted Hilbert–Schmidt numerical radius
نویسندگان
چکیده
Let B(H) be the algebra of all bounded linear operators on a Hilbert space H and let N(⋅) norm B(H). For every 0≤ν≤1, we introduce w(N,ν)(A) as an extension classical numerical radius byw(N,ν)(A):=supθ∈RN(νeiθA+(1−ν)e−iθA⁎) investigate basic properties this notion prove inequalities involving it. In particular, when is Hilbert–Schmidt ‖⋅‖2, present several weighted for operator matrices. Furthermore, give refinement triangle inequality follows:‖A+B‖2≤2w(‖⋅‖2,ν)2([0AB⁎0])−(1−2ν)2‖A−B‖22≤‖A‖2+‖B‖2. Our results extend some theorems due to F. Kittaneh et al. (2019).
منابع مشابه
The numerical radius of a weighted shift operator with geometric weights
Let T be a weighted shift operator T on the Hilbert space 2(N) with geometric weights. Then the numerical range of T is a closed disk about the origin, and its numerical radius is determined in terms of the reciprocal of the minimum positive root of a hypergeometric function. This function is related to two Rogers-Ramanujan identities.
متن کاملthe algorithm for solving the inverse numerical range problem
برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.
15 صفحه اولOn the Numerical Radius and Its Applications*
We give a brief account of the numerical radius of a linear bounded operator on a Hilbert space and some of its better-known properties. Both finiteand infinitedimensional aspects are discussed, as well as applications to stability theory of finite-difference approximations for hyperbolic initial-value problems. 1. DEFINITION, BOUNDS, AND EVALUATION Let H be a Hilbert space over the complex fie...
متن کاملSome numerical radius inequalities with positive definite functions
Using several examples of positive definite functions, some inequalities for the numerical radius of matrices are investigated. Also, some open problems are stated.
متن کاملSome improvements of numerical radius inequalities via Specht’s ratio
We obtain some inequalities related to the powers of numerical radius inequalities of Hilbert space operators. Some results that employ the Hermite-Hadamard inequality for vectors in normed linear spaces are also obtained. We improve and generalize some inequalities with respect to Specht's ratio. Among them, we show that, if $A, Bin mathcal{B(mathcal{H})}$ satisfy in some conditions, it follow...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2023
ISSN: ['1873-1856', '0024-3795']
DOI: https://doi.org/10.1016/j.laa.2023.06.024