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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.10 No.4

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AN EXTENSION OF THE FUGLEDGE-UTNAM THEOREM TO w-HYPONORMAL PERATORS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2003, v.10 no.4, pp.273-277
Cha, Hyung Koo
Cha,, H. K. (2003). AN EXTENSION OF THE FUGLEDGE-UTNAM THEOREM TO w-HYPONORMAL PERATORS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 10(4), 273-277.

Abstract

The Fuglede-Putnam Theorem is that if A and B are normal operators and X is an operator such that AX = XB, then <TEX>$A^{\ast}= X<T^{\ast}B^{\ast}$</TEX>. In this paper, we show that if A is <TEX>$\omega$</TEX>-hyponormal and <TEX>$B^{\ast}$</TEX> is invertible <TEX>$\omega$</TEX>-hyponormal such that AX = XB for a Hilbert-Schmidt operator X, then <TEX>$A^{\ast}X = XB^{\ast}$</TEX>.

keywords
w-hyponormal, Hilbert-Schmidt operator

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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