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This paper is a study of some properties of a collection of bounded linear operators resulting from terraced matrices M acting through multiplication on ℓ^2; the term terraced matrix refers to a lower triangular infinite matrix with constant row segments. Sufficient conditions are found for M to be posinormal, meaning that MM^*=M^*PM for some positive operator P on ℓ^2; these conditions lead to new sufficient conditions for the hyponormality of M. Sufficient conditions are also found for the adjoint M^* to be posinormal, and it is observed that, unless M is essentially trivial, M^* cannot be hyponormal. A few examples are considered that exhibit special behavior.
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참고문헌 (10)
참고문헌 신청
A. Brown / 1965 / Ces aro operators / Acta Sci. Math. (Szeged) 26 : 125 ~ 137
C. S. Kubrusly / 2007 / On posinormal operators / Adv. Math. Sci. Appl. 17 (1) : 131 ~ 147
G. Hardy / 1989 / Inequalities / Cambridge University Press
G. Leibowitz / 1987 / Rhaly matrices / J. Math. Anal. Appl. 128 (1) : 272 ~ 286
H. C. Rhaly, Jr / 1989 / Terraced matrices / Bull. London Math. Soc. 21 (4) : 399 ~ 406
C. S. Kubrusly / 2007 / On posinormal operators / Adv. Math. Sci. Appl. 17 (1) : 131 ~ 147
G. Hardy / 1989 / Inequalities / Cambridge University Press
G. Leibowitz / 1987 / Rhaly matrices / J. Math. Anal. Appl. 128 (1) : 272 ~ 286
H. C. Rhaly, Jr / 1989 / Terraced matrices / Bull. London Math. Soc. 21 (4) : 399 ~ 406
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