%0 Journal Article
%T Space of Operators and Property (<i>MB</i>)
%A Manijeh Esfahani Bahreini
%J Advances in Pure Mathematics
%P 948-953
%@ 2160-0384
%D 2016
%I Scientific Research Publishing
%R 10.4236/apm.2016.613072
%X In this paper, a new class of Banach spaces, termed as Banach spaces with property <span style=\"white-space:nowrap;\">(<i>MB</i>)</span>, will be introduced. It is stated that a space <i>X</i> has property <span style=\"white-space:nowrap;\">(<i>MB</i>)</span> if every <i>V</i> -subset of <span style=\"white-space:normal;\"><i>X*</i></span> is an <span style=\"white-space:normal;\"><i>L</i></span>-subset of <span style=\"white-space:normal;\"><i>X*</i></span> . We describe those spaces which have property (<i>MB</i>) . Also, we show that if a Banach space <span style=\"white-space:normal;\"><i>X</i></span> has property (<i>MB</i>)  and Banach space <span style=\"white-space:normal;\"><i>Y</i></span> does not contain <img src=\"Edit_a00bf6c8-657c-4281-b034-8694d5db97d3.bmp\" alt=\"\" /> , then every operator <img src=\"Edit_ca0107c8-f401-483e-8e44-466609dc0b87.bmp\" alt=\"\" />is completely continuous.
%K &lt
%K i&gt
%K L&lt
%K /i&gt
%K -Sets
%K &lt
%K i&gt
%K V&lt
%K /i&gt
%K -Sets
%K Completely Continuous Operators
%K Unconditionally Converging Operators
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=72770