Analytical study on approximate ?-Birkhoff-James orthogonality

الملخص EN

In this paper, we obtain a complete characterization for the norm and the minimum norm attainment sets of bounded linear operators on a real Banach spaces at a vector in the unit sphere, using approximate ?-Birkhoff-James orthogonality techniques.

As an application of the results, we obtained a useful characterization of bounded linear operators on a real Banach spaces.

Also, using approximate ?-Birkhoff -James orthogonality proved that a Banach space is a reflexive if and only if for any closed hyperspace of , there exists a rank one linear operator such that , for some vectors in and such that ? .Mathematics subject classification (2010): 46B20, 46B04, 47L05.