The paper is concerned with conditions guaranteeing that a bounded operator in a reflexive Banach space is a scalar type spectral operator. The cases where the spectrum of the operator lies on the real axis and on the unit circle are studied separately.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-2, author = {P. A. Cojuhari and A. M. Gomilko}, title = {On the characterization of scalar type spectral operators}, journal = {Studia Mathematica}, volume = {187}, year = {2008}, pages = {121-132}, zbl = {1163.47029}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-2} }
P. A. Cojuhari; A. M. Gomilko. On the characterization of scalar type spectral operators. Studia Mathematica, Tome 187 (2008) pp. 121-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-2/