Results 21 to 30 of about 99 (60)

Topological properties of the block numerical range of operator matrices

, 2020
We show that the block numerical range of an n×n -operator matrix A corresponding to an operator A on the Banach space X with respect to a decomposition X = ∏Xj has at most n connected components.
Agnes Radl, M. Wolff
semanticscholar   +1 more source

Numerical Range on Weighted Hardy Spaces as Semi Inner Product Spaces

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017
The semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.
Heydari Mohammad Taghi
doaj   +1 more source

An observation about normaloid operators

, 2017
Let H be a complex Hilbert space and B(H) the Banach space of all bounded linear operators on H . For any A ∈ B(H) , let w(A) denote the numerical radius of A . Then A is normaloid if w(A) = ‖A‖ .
J. Chan, K. Chan
semanticscholar   +1 more source

Constant norms and numerical radii of matrix powers

Operators and Matrices, 2019
For an n -by-n complex matrix A , we consider conditions on A for which the operator norms ‖Ak‖ (resp., numerical radii w(Ak) ), k 1 , of powers of A are constant.
Hwa-Long Gau, Kuo-Zhong Wang, P. Wu
semanticscholar   +1 more source

Pre-images of Boundary Points of the Numerical Range

, 2014
This paper considers matrices A ∈ Mn(C) whose numerical range contains boundary points generated by multiple linearly independent vectors. Sharp bounds for the maximum number of such boundary points (excluding flat portions) are given for unitarily ...
Timothy Leake, Brian Lins, I. Spitkovsky
semanticscholar   +1 more source

Scalar approximants of quadratic operators with applications

, 2018
Among other results, we find the best scalar approximant of a quadratic operator with respect to the numerical radius and the operator norm. We use these results to give estimates for the numerical radii of products and commutators of quadratic operators.
A. Abu-Omar, P. Wu
semanticscholar   +1 more source

A fiedler-type theorem for the determinant of J-positive matrices

, 2016
In this note we characterize the set of all possible values attained by the determinant of the sum of two J -positive matrices with prescribed spectra, under a natural compatibility condition. Mathematics subject classification (2010): 46C20, 47A12.
N. Bebiano, J. Providência
semanticscholar   +1 more source

On the block numerical range of operators on arbitrary Banach spaces

, 2018
We investigate the block numerical range of bounded linear operators on arbitrary Banach spaces. We show that the spectrum of an operator is always contained in the closure of its block numerical range.
Agnes Radl, M. Wolff
semanticscholar   +1 more source

ON THE MAXIMAL NUMERICAL RANGE OF ELEMENTARY OPERATORS

, 2017
The notion of the numerical range has been generalized in different directions. One such direction, is the maximal numerical range introduced by Stampfli (1970) to derive an identity for the norm of a derivation on L(H). Unlike the other generalizations,
Mati Runji, John Ogonji Agure, F. Nyamwala   +2 more
semanticscholar   +1 more source

On the numerical range of a generalized derivation

, 2017
We examine the relationship between the numerical range of the restriction of a generalized derivation to a norm ideal J and that of its implementing elements.
F. M. Runji, J. O. Agure, F. Nyamwala
semanticscholar   +1 more source