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EXTENSIONS OF POLYNOMIALS ON PREDUALS OF LORENTZ SEQUENCE SPACES

Published online by Cambridge University Press:  27 July 2005

YUN SUNG CHOI ,
KWANG HEE HAN  and
HYUN GWI SONG
YUN SUNG CHOI
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea e-mail: mathchoi@postech.ac.kr, hankh@postech.ac.kr, hyuns@postech.ac.kr
KWANG HEE HAN
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea e-mail: mathchoi@postech.ac.kr, hankh@postech.ac.kr, hyuns@postech.ac.kr
HYUN GWI SONG
Affiliation:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Korea e-mail: mathchoi@postech.ac.kr, hankh@postech.ac.kr, hyuns@postech.ac.kr
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Abstract

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We show that there is a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on the predual $d_*(w,1)$ of a complex Lorentz sequence space $d(w,1)$ to $d^*(w,1)$, but there is no unique norm-preserving extension from $\mathcal{P}(^nd_*(w,1))$ to $\mathcal{P}(^nd^*(w,1))$ for $n\geq3$.

Keywords

46G2546A22
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 2 , May 2005 , pp. 395 - 403
Copyright
2005 Glasgow Mathematical Journal Trust

Footnotes

This research is supported in part by KOSEF Interdisciplinary Research Program Grant 1999-2-102-003-5 of Korea.