J Austral Math Soc Ser A 53 pp9--16, 1992.

M-Cohyponormal Powers of Composition Operators

Satish K. Khurana and Babu Ram

Abstract

Let T_i, i = 1, 2 be measurable transformations which define bounded composition operators C_Ti on L² of a s-finite measure space. Let us denote the Radon-Nikodym dericative of m °T_i^-1 with respect to m by h_i, i = 1, 2. The main result of this paper is that if C*_T1 and C*_T2 are both M-hyponormal with h₁ £ M²(h₂ °T₂) a.e. and h₂ £ M²(h₁ °T₁) a.e., then for all positive integers m, n and p, [(C^m_T1 Cⁿ_T2)^p]* is M^p2(m+n)2-hyponormal. As a consequence, we see that if C*_T is an M-hyponormal compositions operator, then (C*_T)ⁿ is Mⁿ²-hyponormal for all positive integers n.

1991 AMS Subject Classification: primary 47B20; secondary 47B38

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Authors

Satish K. Khurana

Babu Ram

Maharshi Dayanand UNiversity, Rohtak -124001, India.