Inequalities on the spectral radius, operator norm and numerical radius of the Hadamard weighted geometric mean of positive kernel operators
نویسندگان
چکیده
منابع مشابه
Some weighted operator geometric mean inequalities
In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
متن کاملNorm aúaining and numerical radius attaining operators
ABSTRAer. In Ihis note we discusa sorne results oit numerical radius altaining operators paralleling carlier results Oit norm attaining operatora. Eorarbitrary Banach spacesXand Y, the set of (bounded, linear) operatora from Xto Ywhose adjoints altain [heir norms is norm-dense ita [hespaee of ah operators. This theorem. due toW. Zizíer, improves an earlier result by J. Lindenstrauss on the dens...
متن کاملBounds on the spectral radius of Hadamard products of positive operators on lp-spaces
Recently, K.M.R. Audenaert (2010), and R.A. Horn and F. Zhang (2010) proved inequalities between the spectral radius of Hadamard products of finite nonnegative matrices and the spectral radius of their ordinary matrix product. We will prove these inequalities in such a way that they extend to infinite nonnegative matrices A and B that define bounded operators on the classical sequence spaces lp.
متن کاملThe ratios between the spectral norm, the numerical radius and the spectral radius
Recently, Uhlig [Numer. Algorithms, 52(3):335-353, 2009] proposed open questions about the ratios between the spectral norm, the numerical radius and the spectral radius of a square matrix. In this note, we provide some observations to answer these questions. Keywords—Spectral norm, Numerical radius, Spectral radius, Ratios
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 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 and Multilinear Algebra
سال: 2018
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081087.2018.1465885