Roberts Orthogonality On Hilbert Spaces with Numerical Radius Approach

کد مقاله : 1031-SHAA

نویسندگان

Elias Faryad * دانشگاه فردوسی مشهد

چکیده مقاله

‎In this paper, ‎‎‎the Roberts orthogonality is ‎studied with respect to the numerical radius‎. ‎‎ ‎As applications a necessary and sufficient conditions for the numerical range to be symmetric for $2 times 2 $ complex matrices is given‎.‎ Moreover‎, we show that the Roberts orthogonality with respect to the numerical radius implies that ‎‎‎the Roberts, Birkhoff-James and Isosceles orthogonalities for linear operators on a real Hilbert space‎. Among other results, we prove an interrelation between the Roberts orthogonality and the Birkhoff--James orthogonality in the sense of numerical radius for $n times n$ complex matrices.

کلیدواژه ها

Roberts orthogonality‎, ‎Birkhoff--James orthogonality‎, ‎numerical range‎, ‎numerical radius

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