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International Journal of Mathematics and Mathematical Sciences
Volume 15, Issue 3, Pages 617-619
http://dx.doi.org/10.1155/S0161171292000802

Spaces of compact operators which are M-ideals in L(X,Y)

Hanyang University, Seoul 133-791, Korea

Received 10 December 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose X and Y are reflexive Banach spaces. If K(X,Y), the space of all compact linear operaters from X to Y is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X,Y) is isometrically isomorphic to L(X,Y).
{"cc_re__cc_re__cc_by_3_0": [",</mml:mo><mml:mi>Y</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math></h2>\r\n\r\n        <div class=\"author_gp\">\r\n        <a href=\"/24746879/\">Chong-Man Cho</a>      \r\n        </div>\r\n\r\n\r\n         <p>Hanyang University, Seoul 133-791, Korea<br /></p>\r\n           \r\n      \r\n\r\n\r\n\r\n\r\n<p>Received 10 December 1991</p>                \r\n    <div class=\"xml-content\">\r\n        <p>Copyright &#x00A9; 1992 Hindawi Publishing Corporation. This is an open access article distributed under the <a rel=\"license\" href=\"http://creativecommons.org/licenses/by/3.0/\">\r\nCreative Commons Attribution License</a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\r\n        </p>\r\n    </div>\r\n<div id=\"divXMLContent\" class=\"xml-content\">\r\n<h4>Abstract</h4><p>Suppose <mml:math alttext=\"$X$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>X</mml:mi></mml:math> and <mml:math alttext=\"$Y$\" xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"><mml:mi>Y</mml:mi></mml:math> are reflexive Banach spac"], "copyright__copyright__copyright": ["This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.\n\nAbstract\n\nSuppose X and Y are reflexive Banach spaces. If K(X,Y), the space of all compact linear operaters from X to Y is an M-ideal in L(X,Y), the space of all bounded linear operators from X to Y, then the second dual space K(X,Y)** of K(X,Y) is isometrically isomorphic to L(X,Y)."]}