Operator space

<h2 id="equivalent-formulations">Equivalent formulations</h2>
<p>Equivalently, an operator space is a <a href="/facts/Linear_subspace/2wtKTgHL">subspace</a> of a <a href="/facts/C*-algebra/B3tnGHIo">C*-algebra</a>. 
</p>
<h2 id="category-of-operator-spaces">Category of operator spaces</h2>
<p>The <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> of operator spaces includes <a href="/facts/Operator_system/7S47ErPa">operator systems</a> and <a href="/facts/Operator_algebra/4fycDNQ1">operator algebras</a>. For operator systems, in addition to an induced matrix norm of an operator space, one also has an induced matrix order. For operator algebras, there is still the additional <a href="/facts/Ring_(mathematics)/JnCUXz63">ring</a> structure.
</p>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Gilles_Pisier/GzRQq0yx">Gilles Pisier</a></li>
<li><a href="/facts/Operator_system/7S47ErPa">Operator system</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Paulsen, Vern (2002). Completely Bounded Maps and Operator Algebras. Cambridge University Press. p. 26. ISBN 978-0-521-81669-4. Retrieved 2022-03-08. <a href="978-0-521-81669-4" target="_blank">978-0-521-81669-4</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Pisier, Gilles (2003). Introduction to Operator Space Theory. Cambridge University Press. p. 1. ISBN 978-0-521-81165-1. Retrieved 2008-12-18. <a href="978-0-521-81165-1" target="_blank">978-0-521-81165-1</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>Blecher, David P.; Christian Le Merdy (2004). Operator Algebras and Their Modules: An Operator Space Approach. Oxford University Press. First page of Preface. ISBN 978-0-19-852659-9. Retrieved 2008-12-18. <a href="978-0-19-852659-9" target="_blank">978-0-19-852659-9</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Operator space open-in-new

Operator space