Let A ∈ B(H) and B ∈ B(K). We say that A and B satisfy the Fuglede-Putnam theorem if AX = XB for some X ∈ B(K,H) implies A*X = XB*. Patel et al. (2006) showed that the Fuglede-Putnam theorem holds for class A(s,t) operators with s + t < 1 and they mentioned that the case s = t = 1 is still an open problem. In the present article we give a partial positive answer to this problem. We show that if A ∈ B(H) is a class A operator with reducing kernel and B* ∈ B(K) is a class 𝓨 operator, and AX = XB for some X ∈ B(K,H), then A*X = XB*.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-3,
author = {Salah Mecheri},
title = {Fuglede-Putnam theorem for class A operators},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {183-191},
zbl = {06401023},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-3}
}
Salah Mecheri. Fuglede-Putnam theorem for class A operators. Colloquium Mathematicae, Tome 139 (2015) pp. 183-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-3/