Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators
Applications of Orlicz–Pettis theorem in vector valued multiplier spaces of generalized weighted mean fractional difference operators
Abstract In this study, we deal with some new vector valued multiplier spaces $S_{G_{h}}(\sum_{k}z_{k})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>S</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mi>h</mml:mi></mml:msub></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mi>k</mml:mi></mml:msub><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> and $S_{wG_{h}}(\sum_{k}z_{k})$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>S</mml:mi><mml:mrow><mml:mi>w</mml:mi><mml:msub><mml:mi>G</mml:mi><mml:mi>h</mml:mi></mml:msub></mml:mrow></mml:msub><mml:mo>(</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mi>k</mml:mi></mml:msub><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:math> related with $\sum_{k}z_{k}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mo>∑</mml:mo><mml:mi>k</mml:mi></mml:msub><mml:msub><mml:mi>z</mml:mi><mml:mi>k</mml:mi></mml:msub></mml:math> in a normed space Y . Further, we obtain the completeness of these spaces via weakly unconditionally Cauchy series in Y and $Y^{*}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>Y</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:math> …