We deal with space of sequences generalizing the well-known
spaces <mml:math alttext="$w_{\infty}^{p}(\lambda)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>w</mml:mi><mml:mi>&#8734;</mml:mi><mml:mi>p</mml:mi></mml:msubsup><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#955;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>, <mml:math alttext="$c_{\infty}(\lambda, \mu)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>c</mml:mi><mml:mi>&#8734;</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>&#955;</mml:mi><mml:mo>,</mml:mo><mml:mi>&#956;</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:math>,
replacing the operators <mml:math alttext="$C(\lambda)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#955;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> and <mml:math alttext="$\Delta(\mu)$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>&#916;</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>&#956;</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> by their
transposes. We get generalizations of results concerning the
strong matrix domain of an infinite matrix <mml:math alttext="$A$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>.

International Journal of Mathematics and Mathematical Sciences

Calculations on some sequence spaces

Abstract

Copyright