Fuglede-Putnam theorem for class A operators

• Autorzy: Salah Mecheri
• Języki publikacji: EN

Abstrakty

EN

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*.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 47B20: Subnormal operators, hyponormal operators, etc.
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 138
• Numer: 2
• Strony: 183-191

Daty

wydano

2015

Twórcy

autor

Salah Mecheri

• Department of Mathematics, College of Sciences, Taibah University, Medina, Saudi Arabia

Identyfikatory

DOI

10.4064/cm138-2-3