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Some inequalities for semi-inner products on complex Banach Spaces
Abstract
In this paper we establish some inequalities for two sub-semi-inner
products [; ]1 ; [; ]2 for which [; ]2 [; ]1 that are related to SchwarzÂ’s
inequality. Some applications for particular semi-inner products generated by
an element of norm one in the given Banach spaces as well as for some bounded
operators that satisfy a SchwarzÂ’s type condition are given. Some norm and
numerical radius inequalities for operators acting on smooth uniformly convex
Banach spaces with more sugestive examples in the case of complex Hilbert
spaces are also provided.
products [; ]1 ; [; ]2 for which [; ]2 [; ]1 that are related to SchwarzÂ’s
inequality. Some applications for particular semi-inner products generated by
an element of norm one in the given Banach spaces as well as for some bounded
operators that satisfy a SchwarzÂ’s type condition are given. Some norm and
numerical radius inequalities for operators acting on smooth uniformly convex
Banach spaces with more sugestive examples in the case of complex Hilbert
spaces are also provided.
Keywords
Banach spaces, Semi-inner products, SchwarzÂ’s inequality, Operators on Banach spaces, Hilbert spaces, Operators on Hilbert spaces.
DOI: http://dx.doi.org/10.14510%2Flm-ns.v0i0.1433