No Thumbnail Available
Date
2017
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
The studies on Hilbert spaces for the last decade has been of great interest to many mathematicians
and researchers, especially on operator inequalities related to operator norms and numerical radii for
a family of bounded linear operators acting on a Hilbert spaces. Results on some inequalities for normal
operators in Hilbert spaces for instance numerical ranges W(T), numerical radii w(T) and norm ||.||
obtained by Dragomir and Moslehian among others due to some classical inequalities for vectors in
Hilbert spaces. The techniques employed to prove the results are elementary with some special vector
inequalities in inner product spaces due to Buzano, Goldstein, Ryff and Clarke as well as some reverse
Schwarz inequalities. Recently, the new field of operator theory done by Dragomir and Moslehian on
norms and numerical radii for (, ) - normal operators developed basic concepts for our Statement
of the problem on normal transaloid operators. M. Fujii and R. Nakamoto characterize transaloid
operators in terms of spectral sets and dilations and other non-normal operators such as normaloid,
convexoid and spectroid. Furuta did also characterization of normaloid operators. Since none has
done on norms and numerical radii inequalities for (, ) – normal transaloid operators, then our
aim is to characterize (, )- normal transaloid operators, characterize norm inequalities for (
, )- normal transaloid operators and to characterize numerical radii for (, )- normal transaloid
operators. We use the approach of the Cauchy-Schwarz inequalities, parallelogram law, triangle
inequality and tensor products. The results obtained are useful in applications in quantum mechanics.