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BanachJ.Math.Anal.8(2014),no.2,131–138 STRONGCOEFFICIENTQUANTIZATIONPROPERTIESINBANACHSPACES B J M A

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Banach J. Math. Anal. 8 (2014), no. 2, 131–138

B

anach

J

ournal of

M

athematical

A

nalysis ISSN: 1735-8787 (electronic)

www.emis.de/journals/BJMA/

STRONG COEFFICIENT QUANTIZATION PROPERTIES IN BANACH SPACES

KYUGEUN CHO1, JU MYUNG KIM∗2, SUN KWANG KIM3, HAN JU LEE4 To the memory of Professor Edward Odell

Communicated by D. E. Alspach

Abstract. We prove that a dictionary for a Banach spaceX has the strong coefficient quantization property if it has the same property when it restricted on the unit ball of X. We also obtain the same result for the strong net quantization property.

1Bangmok College of Basic Studies, Myong Ji University, Yong-In, Kyung-Ki 449-728, Korea

E-mail address: [email protected]

2 Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea.

E-mail address: [email protected]

3 Department of Mathematics, Kyonggi University , Suwon 443-760, Korea.

E-mail address: [email protected]

4 Department of Mathematics Education, Dongguk University - Seoul, Seoul 100-715, Korea.

E-mail address: [email protected]

Date: Received: Aug. 28, 2013; Accepted: Nov. 23, 2013.

∗ Corresponding author.

2010Mathematics Subject Classification. Primary 46B20; Secondary 46B45.

Key words and phrases. coefficient quantizatioin property, strong coefficient quantizatioin property, net quantizatioin property, strong net quantizatioin property.

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