Domain of Generalized Difference Matrix B(r, s) on Some Maddox’s Spaces

Cafer Aydın, Bilal Altay


In the present paper, the sequence spaces $\widehat{\ell}_\infty(p),~\widehat{c}_0(p)$ and $\widehat{c}(p)$ of non-absolute type have been introduced and proved that the spaces $\widehat{\ell}_\infty(p),~\widehat{c}_0(p)$ and $\widehat{c}(p)$ are linearly isomorphic to the spaces $\ell_\infty(p),~c_0(p)$ and $c(p)$, respectively. The $\beta$- and
$\gamma$-duals of the spaces $\widehat{\ell}_\infty(p),~\widehat{c}_0(p)$ and $\widehat{c}(p)$ have been computed and their basis have been constructed. Finally, some matrix mappings from $\widehat{\ell}_\infty(p),~\widehat{c}_0(p)$ and $\widehat{c}(p)$ to the some sequence spaces of Maddox have been characterized and relationship between the modular $\sigma_p$ and the Luxemburg norm on the sequence space $\widehat{\ell}_\infty(p)$ has been discussed.

Full Text: PDF


  • There are currently no refbacks.

The Thai Journal of Mathematics is supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2021 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|