Joint numerical ranges of operators in semi-Hilbertian spaces

By Hamadi Baklouti, Kais Feki, O. Ahmed. Linear Algebra and its Applications, 2018

127 citations recorded by the source corpus.

Abstract In this paper we aim to investigate the concept of numerical range and maximal numerical range relative to a positive operator of a d-tuple of bounded linear operators on a Hilbert space. Some properties and applications of these sets are studied. Mainly, it is proved that they are convex for d = 1 , this generalizes the well known Toeplitz–Hausdorff Theorem [24] , [16] and Stampfli's result [23] . Moreover, under additional hypotheses, we show that these sets are convex for d ≥ 2 .

Subfields: Applied Mathematics, Computational Theory and Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1d47b5b4c37a71b0dc0e04c87c9c17f18d66c750

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In Applied Mathematics

In Computational Theory and Mathematics

In Statistics and Probability

Kais Feki

Citations in the corpus

A-numerical radius inequalities for semi-Hilbertian space operators (2019, unknown): “, [5, 7, 8, 13, 14, 18, 24, 30, 31, 35]).”
Spectral radius of semi-Hilbertian space operators and its applications (2019, background): “([5]) If T ∈ BA1/2(H), then 1 2 ‖T‖A ≤ ωA(T ) ≤ ‖T‖A.”
Joint normality of operators in semi-Hilbertian spaces (2020, background): “Now, we recall the following definition which is introduced in [14].”
A-Numerical Radius Orthogonality and Parallelism of Semi-Hilbertian Space Operators and Their Applications (2020, unknown): “One may see [7, 8, 10, 11, 17, 22].”
On inequalities for A-numerical radius of operators (2019, unknown): “For T ∈ BA(H), A-numerical radius of T , denoted as wA(T ), is defined as wA(T ) = sup{|〈Tx, x〉A| : x ∈ H, ‖x‖A = 1}, (see [4]).”
A note on the A-numerical radius of operators in semi-Hilbert spaces (2020, background): “One can consult [3,7,11,12] and the references therein.”
Seminorm and numerical radius inequalities of operators in semi-Hilbertian spaces (2019, background): “and cA(T ) = inf { |〈Tx, x〉A| : x ∈ H, ‖x‖A = 1 } , respectively (see [5, 18] and the references therein).”
Some improvements of numerical radius inequalities of operators and operator matrices (2019, background): “For more information we refer the reader to [1, 2, 5].”